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Algebra 1 : Equations of Lines

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Example Questions

Example Question #69 : How To Find The Midpoint Of A Line Segment

Find the midpoint of the line segment with points $\left ( 6, 2\right )$ and $\left ( 5, 16\right )$ .

Possible Answers:

$\left ( 4, 10.5\right )$

$\left ( -5.5, 9\right )$

(5.5, 9 )

$\left ( 11, 3.5\right )$

$\left ( 4, -10.5\right )$

Correct answer:

(5.5, 9 )

Explanation:

In order to solve this problem, you must know the midpoint formula.

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$ .

The first step is to plug in the coordinates of the endpoints given into the formula.

$\left(\frac{6+5}{2},\frac{2+16}{2}\right)$ .

Do the addition written, and you would end up with $\left(\frac{11}{2},\frac{18}{2}\right)$ .

This simplifies to $\left ( 5.5,9\right )$ .

The midpoint of the line segment with coordinates $\left ( 6,2\right )$ and $\left ( 5, 16\right )$ is $\left ( 5.5, 9\right )$ .

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Example Question #901 : Functions And Lines

Find the midpoint of the line segment with the following endpoints:

(-3,-4)(17,6)

Possible Answers:

(1,9)

(-7,-1)

(7,1)

(7,9)

Correct answer:

(7,1)

Explanation:

Finding the midpoint of a line segment only requires that we find the midpoint, or average of both the x and y components. In order to do that, we use the following formula:

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

For the points (-3,-4) and (17,6) plug in the numbers and solve:

$(\frac{-3+17}{2},\frac{-4+6}{2})=(\frac{14}{2},\frac{2}{2})=(7,1)$

This gives a final answer of (7,1)

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Example Question #662 : Equations Of Lines

Find the midpoint of (2,9) and (-1,7) .

Possible Answers:

$\left (\frac{3}{2},8 \right )$

$\left (0,8 \right )$

$\left (\frac{1}{2},8 \right )$

$\left (\frac{3}{2},1 \right )$

$\left (\frac{1}{2},16 \right )$

Correct answer:

$\left (\frac{1}{2},8 \right )$

Explanation:

Write the formula for the midpoint. The midpoint is an order pair.

$(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Substitute the points.

$(x,y) = (\frac{2+ (-1 )}{2},\frac{9+7}{2})$

Simplify the expressions.

$(x,y) = (\frac{1}{2},\frac{16}{2}) = (\frac{1}{2},8)$

The midpoint is located at: $(\frac{1}{2},8)$

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Example Question #663 : Equations Of Lines

Find the midpoint of the line containing endpoings (-1, -1) and (-3, 9).

Possible Answers:

(-4, 8)

(3, -9)

(-2, 5)

(-2, 4)

(2, -10)

Correct answer:

(-2, 4)

Explanation:

To find the midpoint, we use the midpoint formula

$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

where (x_1, y_1) and (x_2, y_2) are the endpoints.

Given the endpoints (-1, -1) and (-3, 9), we can substitute into the formula. We get

$(\frac{-1 + -3}{2}, \frac{-1 + 9}{2})$

$(\frac{-4}{2}, \frac{8}{2})$

(-2, 4)

Therefore, the midpoint is (-2, 4).

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Example Question #664 : Equations Of Lines

Find the midpoint of a line segment with endpoints of (-2, 0) and (-6, -4).

Possible Answers:

(-8, -4)

(-4, -8)

(-4, -2)

(4, 4)

(-2, -4)

Correct answer:

(-4, -2)

Explanation:

To find the midpoint of a line segment given the endpoints, we will use the following formula:

$\text{midpoint} = (\frac{x_1+x_2}{2}, \frac{y_1 + y_2}{2})$

where (x_1, y_1) and (x_2, y_2) are the endpoints given.

Now, we can substitute the points given into the formula. We get

$\text{midpoint} = (\frac{-2+-6}{2}, \frac{0+-4}{2})$

$\text{midpoint} = (\frac{-2 - 6}{2}, \frac{0-4}{2})$

$\text{midpoint} = (\frac{-8}{2}, \frac{-4}{2})$

$\text{midpoint} = (-4, -2)$

Therefore, the midpoint of the endpoints (-2, 0) and (-6, -4) is (-4, -2).

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Example Question #665 : Equations Of Lines

Find the midpoint of the line that contains the following endpoints:

(0, 1) and (-2, -5)

Possible Answers:

(-1, -2)

(1, 2)

(1, -3)

(-2, -1)

(2, 1)

Correct answer:

(-1, -2)

Explanation:

When finding the midpoint of a line, we use the following formula

$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

where (x_1, y_1) and (x_2, y_2) are the endpoints.

Given the points

(0, 1) and (-2, -5)

we can substitute into the formula. We get

$(\frac{0+-2}{2}, \frac{1+-5}{2})$

$(\frac{0-2}{2}, \frac{1-5}{2})$

$(\frac{-2}{2}, \frac{-4}{2})$

(-1, -2)

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Example Question #666 : Equations Of Lines

Find the midpoint of the line containing the following endpoints:

(-1, -1) and (-3, -7)

Possible Answers:

(1, 3)

(-2, -4)

(-1, -3)

(-4, -8)

(2, 4)

Correct answer:

(-2, -4)

Explanation:

When finding the midpoint of a line, we use the following formula

$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

where (x_1, y_1) and (x_2, y_2) are the endpoints.

Given the points

(-1, -1) and (-3, -7)

we can substitute into the formula. We get

$(\frac{-1+-3}{2}, \frac{-1+-7}{2})$

$(\frac{-1-3}{2}, \frac{-1-7}{2})$

$(\frac{-4}{2}, \frac{-8}{2})$

(-2, -4)

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Example Question #661 : Equations Of Lines

Find the midpoint of the line segment containing the two points

(3,8) and (7,4)

Possible Answers:

(3,6)

(5,6)

(2,2)

(5,4)

Correct answer:

(5,6)

Explanation:

To find the midpoint we follow the formula

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Plugging in the points (3,8) and (7,4) for (x_1,y_1) and (x_2,y_2)

$M=(\frac{3+7}{2},\frac{8+4}{2})$

and we get

(5,6)

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Example Question #661 : Equations Of Lines

A line is connected by points (2,5) and (-1,3) on a graph. What is the midpoint?

Possible Answers:

$(-\frac{1}{2},4)$

$(\frac{9}{2},4)$

$(-\frac{3}{2},4)$

$(-\frac{3}{2},1)$

$(\frac{1}{2},4)$

Correct answer:

$(\frac{1}{2},4)$

Explanation:

Write the midpoint formula.

$(x,y) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Let (x_1,y_1) = (2,5) and (x_2,y_2) = (-1,3) .

Substitute the given points.

$(x,y) = (\frac{2+(-1)}{2}, \frac{5+3}{2})$

Simplify the coordinate.

$(x,y) =(\frac{1}{2},4)$

The answer is: $(\frac{1}{2},4)$

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Example Question #668 : Equations Of Lines

Find the midpoint between the following two endpoints: (-2,5) and (4,9) .

Possible Answers:

(1,14)

(2,14)

(2,7)

(-3,-2)

(1,7)

Correct answer:

(1,7)

Explanation:

The midpoint formula is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ . All we need to do is add the x-values and divide by 2, then add the y-values and divide by 2. This leaves us with a midpoint of (1,7) .

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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #69 : How To Find The Midpoint Of A Line Segment

Example Question #901 : Functions And Lines

Example Question #662 : Equations Of Lines

Example Question #663 : Equations Of Lines

Example Question #664 : Equations Of Lines

Example Question #665 : Equations Of Lines

Example Question #666 : Equations Of Lines

Example Question #661 : Equations Of Lines

Example Question #661 : Equations Of Lines

Example Question #668 : Equations Of Lines

All Algebra 1 Resources

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