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Algebra 1 : Functions and Lines

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Example Questions

Example Question #891 : Functions And Lines

Two points, (1,2) and (2,5) , are connected to form a line. What is the midpoint?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Write the midpoint formula. The midpoint is the center of the line segment.

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

Substitute the values of the coordinates.

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) = (\frac{1+2}{2},\frac{2+5}{2})=(\frac{3}{2},\frac{7}{2})$

The midpoint is: $(\frac{3}{2},\frac{7}{2})$

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Example Question #891 : Functions And Lines

Find the midpoint of the line segment formed by the points

(-1, -3) and (3, 3).

Possible Answers:

(1, -1)

(2, 0)

(2, 2)

(1, 0)

(-4, -6)

Correct answer:

(1, 0)

Explanation:

To find the midpoint between two points, 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 points given. So, given the points

(-1, -3) and (3, 3), we can substitute into the formula.

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

$(\frac{2}{2}, \frac{0}{2})$

(1, 0)

Therefore, the midpoint between (-1, -3) and (3, 3) is (1, 0).

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Example Question #893 : Functions And Lines

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

(2,6)(12,12)

Possible Answers:

(14,18)

(7,9)

(12,6)

(6,8)

Correct answer:

(7,9)

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

$(\frac{2+12}{2},\frac{6+12}{2})=(\frac{14}{2},\frac{18}{2})=(7,9)$

This gives a final answer of (7,9)

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Example Question #894 : Functions And Lines

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

(-2,5)(4,7)

Possible Answers:

(6,1)

(1,6)

(3,5)

(8,9)

Correct answer:

(1,6)

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 (-2,5) and (4,7) plug in the numbers and solve:

$(\frac{-2+4}{2},\frac{5+7}{2})=(\frac{2}{2},\frac{12}{2})=(1,6)$

This gives a final answer of (1,6)

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Example Question #895 : Functions And Lines

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

(15,5)(3,5)

Possible Answers:

(6,5)

(9,5)

(9,0)

(12,5)

Correct answer:

(9,5)

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 (15,5) and (3,5) plug in the numbers and solve:

$(\frac{15+3}{2},\frac{5+5}{2})=(\frac{18}{2},\frac{10}{2})=(9,5)$

This gives a final answer of (9,5)

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Example Question #68 : Midpoint Formula

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

(4,9)(-2,-1)

Possible Answers:

(1,4)

(-1,-4)

(-1,4)

(4,0)

Correct answer:

(1,4)

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 (4,9) and (-2,-1) plug in the numbers and solve:

$(\frac{-2+4}{2},\frac{-1+9}{2})=(\frac{2}{2},\frac{8}{2})=(1,4)$

This gives a final answer of (1,4)

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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:

(2,1)(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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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #891 : Functions And Lines

Example Question #891 : Functions And Lines

Example Question #893 : Functions And Lines

Example Question #894 : Functions And Lines

Example Question #895 : Functions And Lines

Example Question #68 : Midpoint Formula

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

All Algebra 1 Resources

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