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Algebra 1 : Midpoint Formula

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Example Questions

Example Question #601 : Equations Of Lines

A line segment on the coordinate plane has endpoints (-5,-4) and (-3,10) . Which quadrant or axis contains its midpoint?

Possible Answers:

Quadrant I

Quadrant III

Quadrant II

The -axis

Quadrant IV

Correct answer:

Quadrant II

Explanation:

The -coordinate of the midpoint is

$\frac{-5 + (-3) }{2} = -4$ ,

which is negative.

The -coordinate of the midpoint is

$\frac{-4+10}{2} =3$ ,

which is positive.

Since the midpoint has a negative -coordinate and a positive -coordinate, the midpoint is in Quadrant II.

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Example Question #21 : Midpoint Formula

A line segment on the coordinate plane has endpoints (5,-4) and (-3,7) . Which quadrant or axis contains its midpoint?

Possible Answers:

Quadrant IV

The -axis

Quadrant III

Quadrant I

Quadrant II

Correct answer:

Quadrant I

Explanation:

The -coordinate of the midpoint is

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

which is positive.

The -coordinate of the midpoint is

$\frac{-4+7}{2} = \frac{3}{2}$ ,

which is positive.

Since both coordinates are positive, the midpoint is in Quadrant I.

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Example Question #22 : Midpoint Formula

Determine the midpoint between the points (-1, 5) and (-7, 3)

Possible Answers:

(4, -4)

(-2, 4)

(-8, 8)

(-4, 4)

(-5, 4)

Correct answer:

(-4, 4)

Explanation:

To find the midpoint you are actually finding the average of the two values and the average of the two values.

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

(-1, 5) , (-7, 3) so we plug our points in to the equation,

$(\frac{-1+(-7)}{2}, \frac{5+3}{2})$

Simplify and divide

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

Midpoint: (-4,4)

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Example Question #851 : Functions And Lines

Find the midpoint of the line segment with endpoints (1.6, 7.3) and ( -1.4, 4.7) .

Possible Answers:

$\left ( 4.45, 1.65\right )$

(1.5, 6)

$\left ( 6, 0.1\right )$

(-1.5,-6)

(0.1, 6)

Correct answer:

(0.1, 6)

Explanation:

Use the midpoint formula:

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

Substitute:

$\frac{x_{1}+x_{2}}{2} =\frac{1.6+(-1.4)}{2} = \frac{0.2}{2} = 0.1$

$\frac{y_{1}+y_{2}}{2}} \right = \frac{7.3+4.7)}{2}} = \frac{12}{2} = 6$

The midpoint is (0.1, 6)

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Example Question #852 : Functions And Lines

Find the midpoint of the line segment with endpoints $\left ( \frac{1}{3}, \frac{5}{6} \right )$ and $\left ( -\frac{5}{6},\frac{2}{3} \right )$ .

Possible Answers:

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

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

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

$\left ( \frac{7 }{12}, -\frac{1 }{12} \right )$

$\left ( -\frac{7 }{12}, \frac{1 }{12} \right )$

Correct answer:

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

Explanation:

Use the midpoint formula:

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

Substitute:

$\frac{x_{1}+x_{2}}{2} = \frac{ \frac{1}{3} + \left (-\frac{5}{6} \right )}{2}= \frac{ \frac{2}{6} - \frac{5}{6} }{2}= \frac{-\frac{3}{6}}{2}= \frac{-\frac{1}{2}}{2} = -\frac{1}{2} \div 2 = -\frac{1}{2} \cdot\frac{1}{2} =-\frac{1}{4}$

$\frac{y_{1}+y_{2}}{2} = \frac{ \frac{5}{6} + \frac{2}{3}}{2} = \frac{ \frac{5}{6} + \frac{4}{6}}{2} = \frac{ \frac{9}{6} }{2}= \frac{ \frac{3}{2} }{2} = \frac{3}{2} \div 2 = \frac{3}{2} \cdot \frac{1}{2} = \frac{3}{4}$

The midpoint is $\left ( -\frac{1 }{4}, \frac{3 }{4} \right )$ .

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Example Question #853 : Functions And Lines

What is the midpoint of a line with endpoints of (9,-3) and (-1,5) ?

Possible Answers:

(-4,-1)

(-1,4)

(1,4)

(4,-1)

(4,1)

Correct answer:

(4,1)

Explanation:

To find the midpoint, you can use the midpoint formula: $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ .

Plug in (9,-3) and (-1, 5) into the formula: $(\frac{9+-1}{2},\frac{-3+5}{2})$ to get (4,1) .

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Example Question #7 : Midpoint Formula

Find the midpoint of the line segment with endpoints (3.6, 9.1) and (7.2, -1.5) .

Possible Answers:

$\left (-1.8, 5.3 \right )$

(5.4, 3.8)

(3.8, 5.4)

$\left (6.35, 2.85 \right )$

$\left (1.8, -5.3 \right )$

$\left (6.35, 2.85 \right )$

$\left (1.8, -5.3 \right )$

$\left (-1.8, 5.3 \right )$

Correct answer:

(5.4, 3.8)

Explanation:

Use the midpoint formula:

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

Substitute:

$\frac{x_{1}+x_{2}}{2} =\frac{3.6+7.2}{2} = \frac{10.8}{2} = 5.4$

$\frac{y_{1}+y_{2}}{2}} \right = \frac{9.1+(-1.5)}{2}} = \frac{7.6}{2} = 3.8$

The midpoint is (5.4, 3.8)

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Example Question #22 : Midpoint Formula

What is the midpoint of a line with endpoints (2,5) and (18,-9)?

Possible Answers:

(10,-2)

(-2,10)

(20,-4)

(6,0)

(-4,20)

Correct answer:

(10,-2)

Explanation:

To find the midpoint of the line, plug the endpoints into the distance formula: $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ . This will give you $(\frac{2+18}{2},\frac{5+-9}{2})$ , or a midpoint of (10,-2) .

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Example Question #12 : How To Find The Midpoint Of A Line Segment

What is the midpoint of a line with endpoints of (12,3) and (28,9)?

Possible Answers:

(8,6)

(20,3)

(12, 8)

(20,6)

(8,3)

Correct answer:

(20,6)

Explanation:

To find the midpoint of a line, plug the endpoints into the midpoint formula:

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

This gives you

$\left(\frac{12+28}{2},\frac{3+9}{2}\right)$

(20,6)

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Example Question #855 : Functions And Lines

What is the midpoint of a line with endpoints of (8,-4) and (20,2) ?

Possible Answers:

(5,-2)

(6,10)

(28,-2)

(14,-1)

(10,4)

Correct answer:

(14,-1)

Explanation:

To find the midpoint of the line, plug the endpoints into the midpoint formula, which is

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

Doing this gives you

$\left(\frac{8+20}{2},\frac{-4+2}{2}\right)$

(14,-1)

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Algebra 1 : Midpoint Formula

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #601 : Equations Of Lines

Example Question #21 : Midpoint Formula

Example Question #22 : Midpoint Formula

Example Question #851 : Functions And Lines

Example Question #852 : Functions And Lines

Example Question #853 : Functions And Lines

Example Question #7 : Midpoint Formula

Example Question #22 : Midpoint Formula

Example Question #12 : How To Find The Midpoint Of A Line Segment

Example Question #855 : Functions And Lines

All Algebra 1 Resources

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