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Algebra 1 : How to find the midpoint of a line segment

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Example Questions

Example Question #61 : How To Find The Midpoint Of A Line Segment

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

(2,1)(8,3)

Possible Answers:

(2,5)

(5,2)

(6,1)

(4,4)

Correct answer:

(5,2)

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 (2,1) and (8,3) plug in the numbers and solve:

$(\frac{2+8}{2},\frac{1+3}{2})=(\frac{10}{2},\frac{4}{2})=(5,2)$

This gives a final answer of (5,2)

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Example Question #651 : Equations Of Lines

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

(-12,-2)(6,4)

Possible Answers:

(-3,1)

(-4,3)

(3,1)

(6,2)

Correct answer:

(-3,1)

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 (-12,-2) and (6,4) plug in the numbers and solve:

$(\frac{-12+6}{2},\frac{-2+4}{2})=(\frac{-6}{2},\frac{2}{2})=(-3,1)$

This gives a final answer of (-3,1)

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Example Question #61 : How To Find The Midpoint Of A Line Segment

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

(2,5)(6,15)

Possible Answers:

(4,10)

(7,6)

(10,4)

(9,3)

Correct answer:

(4,10)

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 (2,5) and (6,15) plug in the numbers and solve:

$(\frac{2+6}{2},\frac{5+15}{2})=(\frac{8}{2},\frac{20}{2})=(4,10)$

This gives a final answer of (4,10)

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Example Question #61 : How To Find The Midpoint Of A Line Segment

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

(3,-2)(9,10)

Possible Answers:

(-2,3)

(3,5)

(6,4)

(4,-6)

Correct answer:

(6,4)

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,-2) and (9,10) plug in the numbers and solve:

$(\frac{3+9}{2},\frac{-2+10}{2})=(\frac{12}{2},\frac{8}{2})=(6,4)$

This gives a final answer of (6,4)

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Example Question #62 : How To Find The Midpoint Of A Line Segment

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

(-2,-4)(4,6)

Possible Answers:

(-3,-2)

(2,2)

(1,1)

(-1,1)

Correct answer:

(1,1)

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 (-2,-4) and (4,6) plug in the numbers and solve:

$(\frac{-2+4}{2},\frac{-4+6}{2})=(\frac{2}{2},\frac{2}{2})=(1,1)$

This gives a final answer of (1,1)

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Example Question #63 : How To Find The Midpoint Of A Line Segment

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

(12,5)(8,7)

Possible Answers:

(20,6)

(12,9)

(7,15)

(10,6)

Correct answer:

(10,6)

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 (12,5) and (8,7) plug in the numbers and solve:

$(\frac{12+8}{2},\frac{5+7}{2})=(\frac{20}{2},\frac{12}{2})=(10,6)$

This gives a final answer of (10,6)

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Example Question #64 : How To Find The Midpoint Of A Line Segment

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

(7,7)(1,1)

Possible Answers:

(3,3)

(5,5)

(4,4)

(8,8)

Correct answer:

(4,4)

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 (7,7) and (1,1) plug in the numbers and solve:

$(\frac{7+1}{2},\frac{7+1}{2})=(\frac{8}{2},\frac{8}{2})=(4,4)$

This gives a final answer of (4,4)

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Example Question #65 : How To Find The Midpoint Of A Line Segment

Find the midpoint of a line with the endpoings (0, 5) and (7, 1).

Possible Answers:

(3.5, 3)

(3, 3.5)

(-7, 4)

(7, 6)

(4, 2)

Correct answer:

(3.5, 3)

Explanation:

When finding the midpoint between two points, 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 points given.

Knowing this, we can substitute the values into the formula. We get

$(\frac{0 + 7}{2}, \frac{5 + 1}{2})$

$(\frac{7}{2}, \frac{6}{2})$

(3.5, 3)

Therefore, (3.5, 3) is the midpoint.

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Example Question #10 : Midpoint Formula

Find the midpoint of a line with the endpoings (3, 4) and (-1, -1).

Possible Answers:

(4, 5)

(-3, -4)

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

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

(2, 3)

Correct answer:

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

Explanation:

When finding the midpoint between two points, we use the midpoint formula

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

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

Knowing this, we can substitute the values into the formula. We get

$\left(\frac{3 + -1}{2}, \frac{4 + - 1}{2}\right)$

$\left(\frac{3-1}{2}, \frac{4-1}{2}\right)$

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

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

Therefore, $\left(1, \frac{3}{2}\right)$ is the midpoint.

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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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Algebra 1 : How to find the midpoint of a line segment

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #61 : How To Find The Midpoint Of A Line Segment

Example Question #651 : Equations Of Lines

Example Question #61 : How To Find The Midpoint Of A Line Segment

Example Question #61 : How To Find The Midpoint Of A Line Segment

Example Question #62 : How To Find The Midpoint Of A Line Segment

Example Question #63 : How To Find The Midpoint Of A Line Segment

Example Question #64 : How To Find The Midpoint Of A Line Segment

Example Question #65 : How To Find The Midpoint Of A Line Segment

Example Question #10 : Midpoint Formula

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

All Algebra 1 Resources

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