Question 4 of 9
Triangle EFG has vertices E(-4, 1), F(-3,-2), and G(2, 1). Find the coordinates of the image of points E
F, and G'after a translation 2 units down.

Answers

Answer 1

The coordinates of the image of point E after a translation 2 units down are (-4, -1).

The coordinates of the image of point F after a translation 2 units down are (-3, -4).

The coordinates of the image of point G after a translation 2 units down are (2, -1).

How to translate coordinates?

To translate coordinates in a two-dimensional plane, you need to know the translation vector. A translation vector is a pair of numbers (a, b) that indicates the amount of movement in the x-direction and y-direction.

To translate a point (x, y) by the translation vector (a, b), you can use the following formulas:

x' = x + a

y' = y + b

Where x' and y' are the new coordinates of the point after the translation.

A translation is a transformation that moves a figure a certain distance in a certain direction without rotating or reflecting it. In this case, we are asked to translate the triangle EFG 2 units down. This means that we need to move the triangle down 2 units on the y-axis.

To translate a point (x, y) down 2 units, we can add -2 to the y-coordinate. The new coordinates of the point will be (x, y - 2).

The coordinates of E are (-4, 1), so the coordinates of E' after the translation are (-4, 1-2) = (-4,-1)

The coordinates of F are (-3,-2), so the coordinates of F' after the translation are (-3,-2-2) = (-3,-4)

The coordinates of G are (2, 1), so the coordinates of G' after the translation are (2,1-2) = (2,-1)

So the new coordinates for the triangle EFG' after the translation are:

E'(-4,-1)

F'(-3,-4)

G'(2,-1)

It's important to notice that the x-coordinates didn't change because we are only translating the triangle down, on the y-axis.

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Related Questions

How to find slope intercept form with one point and parallel?

Answers

If two parallel lines have slopes of m(1) and m(2), and if it is known that both lines are perpendicular, then we get m(1) = m(2).

The slope of parallel lines is the same. Since all of the parallel lines are similarly inclined with respect to the positive x-axis, their slopes are also identical. When two parallel lines' slopes are written as m(1), m(2), we get m(1) = m(2).

Equal coefficients for x and y are present in the equations that represent parallel lines. ax + by + c(2) = 0 is the line parallel to ax + by + c(1) = 0. According to observation, the coefficients of x and y in both equations are equivalent.

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Question 3 of 10
What is the factorization of the trinomial below?
x³-2x²-35x
OA. x(x-7)(x-5)
O B. (x²-7)(x+5)
O C. x(x-7)(x+5)
D. (x-7)(x+5)

Answers

Answer:

C. x(x-7)(x+5)

Step-by-step explanation:

consider the more realistic case where students choose how much time to spend in a preparation course, and you can only randomly sample sat and hours from the population. write the population model as sat

Answers

In this scenario, the population model would be written as:

SAT = β0 + β1 * Hours + ε

where:

SAT represents the SAT score of the studentsHours represents the number of hours the students spend in the preparation courseβ0 is the intercept termβ1 is the slope coefficient representing the relationship between the number of hours spent in the preparation course and the SAT scoreε is the error term, representing the unpredictable factors that affect SAT scores and are not explained by the number of hours spent in the preparation course.

This model represents the underlying relationship between SAT scores and the number of hours spent in the preparation course for the entire population. By randomly sampling data from this population, you can use this model to make inferences about the population parameters (β0, β1) and make predictions about SAT scores based on the number of hours spent in the preparation course.

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What is 871.816 divided by 7618.882 ?

Answers

Answer:

-0,8777 the answer is at least it seems

Step-by-step explanation:

0.1144283374 is its answer..

27
of the students in
100
6th grade said they
have one sibling. What
27
percent is equal to?
100
11»
>>> FRACTION, DECIMAL, PERCENT
E

Answers

The 27 percent is equal to 27/100 as a fraction, 0.27 as a decimal and 27% as a percentage.

What is percentage?

A percentage is a way of expressing a number as a fraction of 100. It is often used to express a proportion or ratio of one number to another, usually with respect to a whole. A percentage is denoted by the symbol "%". It can be represented as a decimal or a fraction.

27 out of 100 students in 6th grade said they have one sibling.

As a fraction, this is 27/100.

As a decimal, this is 0.27

As a percentage, this is 27%

Hence, 27 percent is equal to 27/100 as a fraction, 0.27 as a decimal and 27% as a percentage.

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Are vertical lines negative?

Answers

Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

Now, According to the question :

What is Vertical line?

A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to x-axis and goes straight, left and right.

Is a vertical line positive or negative?

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Hence, Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

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Round 20282.93 to the nearest thousand

Answers

The number after rounding off the given decimal number is

20283.

What is rounding of a number?

Rounding means making a number simpler but keeping its value close to what it's original value. The result is less accurate, but easier to use.

Given is the decimal number as -

20282.93

The given number is -

20282.93

20282.9           {3 < 5}

20283              {9 > 5}

Therefore, the number after rounding off the given decimal number is

20283.

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In a certain​ chemical, the ratio of zinc to copper is 4 to 19. A jar of the chemical contains 741 of copper. How many grams of zinc does it​ contain?

Answers

Using the ratio formula the amount of zinc in the jar of chemical containing 741 grams of copper is 156 grams.

What is ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other.

The amount in ratio of zinc in a chemical is = 4

The amount in ratio of copper in a chemical is = 19

The actual weight of copper in the jar of the chemical is = 741

The actual weight of zinc in the jar of the chemical is = x

Use the formula for ratio -

A : B = A' : B'

Substitute the values in the equation -

4 : 19 = x : 741

4/19 = x/741

Simplify the equation to get the amount of zinc -

19 × x = 4 × 741

19x = 4 × 741

x = (4 × 741)/19

x = 4 × 39

x = 156

Therefore, the amount of zinc in the jar is 156 grams.

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15x divide 5xy what is it

Answers

Answer: 3/y

Step-by-step explanation:

Answer:

3/

Step-by-step explanation:

15x/15xy

cancel x on the numerator with x in denominator then divide 15 by 5 to get 3 as numerator and y as denominator.

Help me ;-;
Enter a number in each box so that the expressions are equivalent.
(A) 0.8 (2x + x) + 3(7 - 4.1x) = x + 21

(B) 12
1
2
(6x + 22y) = x + y

(C) (3x - ) - (6x + 1) = -3x - 2

(D) 112
1
2
x + 27y = (12
1
2
x + 9y)

Answers

Therefore , the solution of the given problem of linear equation is  x's coefficient is -9.9,x's coefficient is 75  and  y's coefficient is 275.

How a linear equation is defined ?

A model of linear regression is one that applies the formula y=mx+b. B is the slope, and m is the y-intercept. Ignoring the fact that while both y and y are distinct components, the previous sentence is frequently referred as a "mathematical formula with two variables." Bivariate linear equations only have two variables. The application domains of linear equations have zero solutions in all cases.

Here,

Given :

=>0.8 (2x + x) + 3(7 - 4.1x) = __x + 21

=>0.8(3x) + 21 - 12.3x = __x + 21

=>2.4x + 21 - 12.3x = __x + 21

=>-9.9x + 21 = __x + 21

=> -9.9

=> 12 1/2 (6x + 22y) = x + y

=> 75x + 275y = x + y

Therefore , the solution of the given problem of linear equation is  x's coefficient is -9.9,x's coefficient is 75  and  y's coefficient is 275.

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4x³ - 7x + 3; x-1

Enter the Zeros of the functions in Numerical Order

Answers

Answer:

Step-by-step explanation:

145

how do you add algebraic expressions?

Answers

The process of gathering similar phrases and adding them is known as addition of algebraic expressions. To determine the final expression for the above problems, locate, add, and sum the coefficients of similar terms.

What is the sum of algebraic expressions?The process of gathering similar phrases and adding them is known as addition of algebraic expressions. To determine the final expression for the above problems, locate, add, and sum the coefficients of similar terms. Our explanations on how to add algebraic expressions are simple and straightforward. To solve the addition of algebraic expressions, we even provide various examples for various approaches. In order to solve algebraic expressions, it is therefore best to check the practice problems, answers, and explanations for each problem.Incorporate 5a + 7b - 6c, b + 2c - 3a, and 2a - 5b - 3c.The given phrases are 5a + 7b - 6c, 2a - 5b - 3c, and b + 2c - 3.There are three accessible variables when using the horizontal method.Finding the total of all terms' numerical coefficients requires noting similar terms first and then summing them all.

3a + 2a - 5b - 3c, 5a + 7b - 6c + b + 2c, and 2c + b.

Combine phrases that are similar.

6c + 2c - 3c. 5a - 3a + 2a + 7b + b.

Next, total up all terms' numerical coefficients.

4a + 3b – 7c.

It is 4a + 3b - 7c that must be expressed.The given expressions should be written in rows using the column method, with the same order. Add similar terms in a column after noting them down below one another.Put the expressions in a different order.

5a + 7b – 6c, - 3a + b + 2c, 2a - 5b - 3c

Similar terms should be written down below one another and added in columns.

+ 5a + 7b - 6c - 3a + b + 2c + 2a - 5b - 3c

4a + 3b – 7c

The necessary equation is 4a + 3b - 7c.

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What do u times or multiply the 8 by?

Answers

Answer: 9

6/8 = 9/12

What is the domain of the function below?

a) x < 2
b) x ≤ 3
c) x ≤ 2
d) All real numbers

Answers

The domain of the graphed function is:

D: x ≥ 2

What is the domain of the graphed function?

For a function y = f(x), we define the domain as the possible inputs, this is, the possible values of x.

To find the domain, we need to look at the horizontal axis, we can see that the minimum is the leftmost value, which is (2, 3), and it is marked with a  colored dot, so the value x = 2 belongs to the domain.

Then, the line extends to the right side, so the domain is the set of all real values larger than x = 2

The domain is:

D: x ≥ 2

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I really need help with this ☹️

Answers

a) to find the slope, select 4 points, like (1,22) and (2,29), then use the rule y-y/x-x so 29-22/2-1 (remember if you use y1 then you have to use x1 in bottom) so the slope is = 7

b) y=mx+c (equation formation) m=slope and c= y intercept, so replace y with 22 and the x with 1 and the m with the slope we found earlier, (7) so it’ll be 22=(7)(1)+c (22=7+c), lastly take 7 to the other side which will be 22-7=c and so y intercept is 15

c) previously we found the y intercept and slope so the equation = y = 7x+15

Slope: 7

Y-intercept: 15

Equation: y = 7x + 15

To find the slope, start with finding the change in y and change in x.

If you look at the table, you can see the x values constantly change by 1. You can also see that the y values constantly change by 7.

Slope = change in y ÷ change in x

Slope = 7 ÷ 1

Slope = 7

To find the y-intercept, look at the table and see what y is when x is 0, which is 15.

The standard form of a linear equation is y = mx + b, m being the slope and b being the y-intercept. We have already found those values, so we can substitute them in to get y = 7x + 15.

Mackenzie is trying to find the height of a radio antenna on the roof of a local
building. She stands at a horizontal distance of 29 meters from the building.
The angle of elevation from her eyes to the roof (point A) is 24° and the
angle of elevation from her eyes to the top of the antenna (point B) is 32°. If
her eyes are 1.71 meters from the ground, find the height of the antenna (the
distance from point A to point B). Round your answer to the nearest meter if
necessary.

Answers

The antenna Is[tex]$4.6 \mathrm{~m}$[/tex] high

Steps on how to determine the radio antennas' height?Height of the base station antenna (h1) is 30.48 metres (100 ft) At the antenna, base-station power is 10 watts (40 dBm) Gt = 6 dB more than the dipole gain for the base-station antenna (6 dBd). The FM band can be operated more effectively with short antennas that are coiled or have a coil at the base. The AM broadcast band requires long and growing antennas. Basically, they are lengthy conductors—the longer, the better.

To find the distance H, we make use of the relationship

[tex]& \frac{H}{33 m}=\tan 33^{\circ} \\[/tex]

[tex]& \Longrightarrow H=33 m \cdot \tan 33^{\circ}[/tex]

To find the distance h, we make use of the relationship

[tex]& \frac{h}{33 m}=\tan 27^{\circ} \\[/tex]

[tex]& \Longrightarrow h=33 m \cdot \tan 27^{\circ}[/tex]

Thus, the distance H - h, or the height of the radio antenna, can be found as follows

[tex]& H-h=33 m \cdot \tan 33^{\circ}-33 m \cdot \tan 27^{\circ} \\[/tex]

[tex]& =33 m \cdot\left(\tan 33^{\circ}-\tan 27^{\circ}\right) \\[/tex]

[tex]& =33 m \cdot(0.6494-0.5095) \\[/tex]

[tex]& =33 m \cdot 0.1399 \\[/tex]

[tex]& =4.6167 m \approx 4.6 m[/tex]

The antenna Is[tex]$4.6 \mathrm{~m}$[/tex] high

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If a point is chosen inside the large circle, what is the probability that it will also be inside the small circle?

[?]%

Answers

A point near the center of a circle can be situated under the area covered by radius R/2.

So, the favourable outcomes = [π x (R/2)^2]

Now, a point inside a circle can be situated under area covered by radius R.

So, total outcomes = [π x ( R) ^2]

Hence, required probability,

= [ π x (R/2)^2]/[π x (R) ^2]

=1/4

=2.5

Radius

Radius is defined as a line segment joining the center to the boundary of a circle or a sphere. The length of the radius remains the same from the center to any point on the circumference of the circle or sphere. It is half of the length of the diameter.

What is Radius

In geometry, the radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary. It is an important part of circles and spheres which is generally abbreviated as 'r'. The plural of radius is "radii" which is used when we talk about more than one radius at a time. The largest line segment in a circle or sphere joining any points lying on the opposite side of the center is the diameter, and the length of the radius is half of the length of the diameter. It can be expressed as d/2, where 'd' is the diameter of the circle or sphere.

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Please help quickly! TV is a medsegment of UWX
if WX=3s+77 and TV=2s+42, what is TV

Answers

The length of TV is 40 units.

What is Triangle Midsegment theorem?

The section connecting a triangle's two sides at their midpoints is parallel to and only half as long as the third side.

Given a triangle ABC, let's draw a line segment connecting the midpoints of two of the sides, say AB and BC.

Then by Triangle Midsegment Theorem,

DE = (1/2)AC. DE is parallel to AC

Given:

WX = 3s+ 77 and TV = -2s + 42

As, we know a midsegment connecting two sides of a triangle is parallel to the third side and is half as long.

VT = 1/2 WX

-2s + 42 = 1/2 ( 3s + 77)

-4s + 84 = 3s + 77

84- 77= 3s + 4s

7 = 7s

s = 1

Hence, length of TV = -2(1)+ 42 = 40 units

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The prism below is made of cubes that measure 1/2 of a centimeter on one side. What is the volume?

Answers

The volume of the prism attached in the figure is calculated to be

A. 9/4 cubic cm

How to solve for the volume of the prism

The prism is formed by cubes having a dimension of 1/2 of a centimeter

Using this dimension it can be deduced from the figure that the

the width has 2 units = 2 * 1/2 = 1 cm

the length has 3 units = 3 * 1/2 = 1.5 cm

the height has 3 units = 3 * 1/2 = 1.5 cm

volume of a prism is solved by the formula

= length * width * height

= 1.5 * 1 * 1.5

= 9/4 cubic cm

the volume of the prism is 9/4 cubic units

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Erin and Frannie entered a rug design contest. The rules stated that the rug’s dimensions must be 32 inches × 45 inches and that they must be rectangular. They drew the following for their entries.


Draw the rug, find each partial product. (use the area model)

Answers

The area of the rug is 1,440 square inches and the sum of partial product is always equal to the area, 1440 square inches.

The area of the rug using the formula:

length x width = area.

The area of the rug is:

32 inches x 45 inches = 1440 square inches.

Refer figure for Erin and Frannie's design. Consider Erin's design

green = 30×5 = 150

red = 2×5 = 10

blue = 2×40 = 80

yellow = 30×40 = 1200

total area = green + red + blue + yellow

= 150 + 10 + 80 + 1200

= 1,440

Now consider Frannie's design

red = 5×1 = 5

blue = 35×1 = 35

green = 5×30 = 150

yellow = 35×30 = 1050

total area = 4red + 2blue + 2green + yellow

= 4×5 + 2×35 + 2×150 + 1050

= 20 + 70 + 300 + 1050

= 1,440

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The point of intersection of concurrent lines is called the?

Answers

The point of intersection of concurrent lines is called the point of concurrency.

Concurrent lines are lines that intersect at a single common point. This point of intersection is also known as the point of concurrency.

It can also be said that concurrent lines are lines that pass through a common point and this point is known as the point of intersection or point of concurrency.

In geometric figures, there are some special point of concurrency. For example, in a triangle, there are three special point of concurrency: the incenter, the circumcenter, and the orthocenter. The incenter is the center of the inscribed circle, the circumcenter is the center of the circumcircle and orthocenter is the point where the three altitudes of the triangle intersect.

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a buyer for a specialty clothing manufacturer must buy at least 2000 bales of cotton that weigh at least 420 kilograms per bale. a cotton broker has a shipment of 100,000 bales with weights that are normally distributed with a mean of 376 kilograms and a standard deviation of 22 kilograms. how many bales should the buyer purchase to ensure that he has at least 2000 bales that weigh 420 kilograms each?

Answers

The buyer should purchase 87913 bales to ensure that he has at least 2000 bales that weigh 420 kilograms each.

For having a bale of 420 and above,

we calculate standard deviation using below information

(420 - 376 /22) = 0.02275 = 2.275% chance of having a bale of 420+ kg

To find out the number of bales to pe precise,

2000/0.02275 = 87912.1 so you'll need at the very least 87913 bales to be reasonably certain.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

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Over the next 17 months you have to read more than 102 books. You have to read x books per month. The inequality 17x > 102 represents this situation. Solve the inequality to find the number of books you have to read per month.

how many books do you have to read more than per month

Answers

Hello! I won't be putting the answer to this question, not sure what format this is (test/homework.)  Just want to be clear!  So I'll be explaining what to do but the answer is for you to find.  ;)

Step-by-step explanation:  17x > 102, divide both sides by 17 to isolate the x.
17x/17 > 102/17

I'll leave you with that!  ;D

Answer:

More than 6 books per month.

Step-by-step explanation:

Given variable:

Let x be the number of books you have to read per month.

Given information:

Over the next 17 months you have to read more than 102 books.

Therefore, the inequality to represent the given information is:

17x > 102

To solve the inequality, divide both sides by 17:

⇒ 17x ÷ 17 > 102 ÷ 17

⇒ x > 6

Therefore, you have to read more than 6 books per month.

What are the 3 trigonometric ratios?

Answers

The three most common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

A survey of 169 law firms in a country found that the average hourly billing rate for partners was $607 what is the population and the sample?

Answers

The population in this case would be all of the law firms in the country.

The sample is the group of law firms that were surveyed, which is 169 firms.

The average hourly billing rate of $607 is the sample statistic.

In statistics, a population is the entire group of individuals or objects that we are interested in studying. In this case, the population would be all of the law firms in the country. The population can include all possible values, characteristics, and attributes of interest.

A sample, on the other hand, is a subset of the population that we actually collect data from. In this case, the sample is the group of 169 law firms that were surveyed. The sample is used to represent the population and to make inferences about the population.

Also, the sample statistics such as the average hourly billing rate of $607, is an estimate of the population parameters such as population mean, which is the average hourly billing rate of all law firms in the country.

In summary, population represents the entire group of law firms in the country, and the sample is a subset of law firms surveyed and the sample statistic such as the average hourly billing rate of $607 is an estimate of the population parameter such as population mean.

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Identify the properties used in solving the inequality.

Answers

The inequality is resolved using the addition and division characteristics.The addition, subtraction, multiplication, and division operations all function as methods for solving equations.

Determine the attributes that were used to solve the inequality ?

Describe inequality.The addition, subtraction, multiplication, and division operations all function as methods for solving equations.

Finding the value of the unknown variable might be as easy as adding, subtracting, multiplying, or dividing the two sides of an equation.

Inequality is the relationship between two expressions or values that are not equal to one another.

3x - 2 > -4 is the inequality that is given.

Greater than minus four is three times x minus two.

The addition property is used to add +2 on both sides.

3x – 2 +2 > -4+2

3x>-2

By dividing +3 on both sides, we can be employing the division property.

x>-2/3

Therefore, the inequality is resolved using the addition property and division property.

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7. A toy is made up of cylindrical rings stacked
on a base, as shown in the diagram. The
diameter of Ring 1 is 87% of the diameter of the
base. For Ring 2 through Ring 7, the diameter
of each ring is 87% of the diameter of the ring
directly below it.
7
G
2
The diameter of the base is 5 inches. Which
function can be used to find the diameter in
inches of Ring r, wherel≤r≤7 ?
F d(r) = 5(0.87)
G_ d(r) = 0.87(r-5)
H_ d(r) = 0.87(5)
J d(r) = 5(r-0.87)

Answers

The function that can be used to find the diameter in inches of Ring r, is option F: d(r) = 5× (0.87)^r.

What is diameter?

A circle is a 2D form in geometry in which all of the points on its surface are equally spaced from its centre. The radius is the length from any point on the surface to the centre. Similar to this, the diameter of a circle is defined as the distance through its centre between any two points on its surface.

It is given that the diameter of base is 5 inches.

The diameter of ring 1 is 87% of diameter of base -

⇒ diameter of ring 1 = 87% of 5 inch

= 5 × 87/100

Diameter of ring 1 = 5 × 0.87 inch

Now, diameter of ring 2 is 87% of diameter of ring 1

⇒ diameter of ring 2 = 87% of 5 × 0.87 inch

= 5 × 0.87 ×87/100

= 5 × 0.87 × 0.87

Diameter of ring 2 = 5× (0.87)²

Now, diameter of ring 3 is 87% of diameter of ring 2

⇒ diameter of ring 3 = 87% of 5 × (0.87)² inch

= 5 × (0.87)² ×87/100

= 5 × (0.87)² × 0.87

Diameter of ring 3= 6× (0.9)³

Therefore, the diameter of ring r = 5× (0.87)^r.

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What is the nature of the roots of the quadratic equation â 3x² 10x 7 â 3 0?

Answers

The roots of the equation √3x²+10x +7√3 = 0 are -7/√3 or -3.

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The general form of the quadratic equation is:  ax² + bx + c = 0,

where x is an unknown variable and a, b, c are numerical coefficients.

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics.

Given that,

√3x²+10x +7√3 = 0

=> √3x²+3x+7x +7√3 = 0

=> √3(x+√3) +7(x+√3) = 0

=> √3 +7 = 0 or x+√3 = 0

x = -7/√3 or -3 are the two roots of the equation.

Thus, The roots of the equation √3x²+10x +7√3 = 0 are -7/√3 or -3.

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What is a quotient example?

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Answer: A quotient is an answer to a division problem

Step-by-step explanation: Exaple: 2/3=0.6666666666666.... in this problem 0.66666666666666666666666666666666666 is the quotient

Determine whether AB←→ and CD←→− are parallel, perpendicular, or neither. A(1, 5), B(4, 4), C(9, -10), D(-6, -5)

Answers

The lines [tex]\overleftrightarrow{AB}[/tex] with points on the line A(1, 5), and B(4, 4) and the line [tex]\overleftrightarrow{CD}[/tex] with points C(9, -10), D(-6, -5), have equal slopes and are therefore; parallel

[tex]\overleftrightarrow{AB}[/tex] is parallel to [tex]\overleftrightarrow{CD}[/tex]

What are parallel lines?

Parallel lines are lines in which the distance between them remain the same as they extend contionuously.

The two lines are parallel, perpendicular, or neither, depending on their slope.

The lines  [tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex] are parallel, if their slope are the same

The lines  [tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex]  are perpendicular if the slope of  [tex]\overleftrightarrow{AB}[/tex] is the negative reciprocal of the slope of [tex]\overleftrightarrow{CD}[/tex]

The lines  [tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex] are neither parallel nor perpendicular if their slope are neither equal nor the negative inverse of the other.

The slope of a line passing through the points (x₁, y₁), (x₂, y₂) can be found using the formula;

[tex]Slope=\frac{y_2 - y_1}{x_2 - x_1}[/tex]

The slopes of the line [tex]\overleftrightarrow{AB}[/tex] and line [tex]\overleftrightarrow{CD}[/tex] are therefore

The slope of line [tex]\overleftrightarrow{AB}[/tex]  = (4 - 5)/(4 - 1) = -1/3

Slope of [tex]\overleftrightarrow{CD}[/tex] = (-5 - (-10))/(-6 - 9) = -1/3

The slope of the lines [tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex] are the same therefore, the lines  [tex]\overleftrightarrow{AB}[/tex] and [tex]\overleftrightarrow{CD}[/tex] are parallel

Learn more about parallel and perpendicular lines here: https://brainly.com/question/29526529

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