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Algebra 1 : Functions and Lines

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Example Questions

Example Question #851 : Functions And Lines

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

Possible Answers:

$\displaystyle (-1.5,-6)$

$\displaystyle (1.5, 6)$

$\left ( 4.45, 1.65\right )$ $\displaystyle \left ( 4.45, 1.65\right )$

$\left ( 6, 0.1\right )$ $\displaystyle \left ( 6, 0.1\right )$

$\displaystyle (0.1, 6)$

Correct answer:

$\displaystyle (0.1, 6)$

Explanation:

Use the midpoint formula:

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

Substitute:

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

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

The midpoint is $\displaystyle (0.1, 6)$

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Example Question #852 : Functions And Lines

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Use the midpoint formula:

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

Substitute:

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

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

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

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Example Question #853 : Functions And Lines

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

Possible Answers:

(4,1) $\displaystyle (4,1)$

(-1,4) $\displaystyle (-1,4)$

(4,-1) $\displaystyle (4,-1)$

(-4,-1) $\displaystyle (-4,-1)$

(1,4) $\displaystyle (1,4)$

Correct answer:

(4,1) $\displaystyle (4,1)$

Explanation:

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

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

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Example Question #1 : Midpoint Formula

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

Possible Answers:

$\displaystyle (3.8, 5.4)$

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

$\left (6.35, 2.85 \right )$ $\displaystyle \left (6.35, 2.85 \right )$

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

$\displaystyle (5.4, 3.8)$

$\left (6.35, 2.85 \right )$ $\displaystyle \left (6.35, 2.85 \right )$

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

Correct answer:

$\displaystyle (5.4, 3.8)$

Explanation:

Use the midpoint formula:

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

Substitute:

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

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

The midpoint is $\displaystyle (5.4, 3.8)$

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Example Question #854 : Functions And Lines

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

Possible Answers:

(20,-4) $\displaystyle (20,-4)$

(6,0) $\displaystyle (6,0)$

(-2,10) $\displaystyle (-2,10)$

(-4,20) $\displaystyle (-4,20)$

(10,-2) $\displaystyle (10,-2)$

Correct answer:

(10,-2) $\displaystyle (10,-2)$

Explanation:

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

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Example Question #855 : Functions And Lines

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

Possible Answers:

(12, 8) $\displaystyle (12, 8)$

(20,3) $\displaystyle (20,3)$

(20,6) $\displaystyle (20,6)$

(8,3) $\displaystyle (8,3)$

(8,6) $\displaystyle (8,6)$

Correct answer:

(20,6) $\displaystyle (20,6)$

Explanation:

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

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

This gives you

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

(20,6) $\displaystyle (20,6)$

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Example Question #21 : How To Find The Midpoint Of A Line Segment

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

Possible Answers:

(5,-2) $\displaystyle (5,-2)$

(14,-1) $\displaystyle (14,-1)$

(6,10) $\displaystyle (6,10)$

(28,-2) $\displaystyle (28,-2)$

(10,4) $\displaystyle (10,4)$

Correct answer:

(14,-1) $\displaystyle (14,-1)$

Explanation:

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

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

Doing this gives you

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

(14,-1) $\displaystyle (14,-1)$

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Example Question #22 : How To Find The Midpoint Of A Line Segment

What is the midpoint of a line segment with endpoints of (-7,4) $\displaystyle (-7,4)$ and (3,16) $\displaystyle (3,16)$?

Possible Answers:

(-2,10) $\displaystyle (-2,10)$

(-4,20) $\displaystyle (-4,20)$

(20,-4) $\displaystyle (20,-4)$

(-1,5) $\displaystyle (-1,5)$

(10,-2) $\displaystyle (10,-2)$

Correct answer:

(-2,10) $\displaystyle (-2,10)$

Explanation:

To find the midpoint of the line segment, plug in the endpoints to the midpoint formula, which is

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

This gives you

$\left(\frac{-7+3}{2},\frac{4+16}{2}\right)$ $\displaystyle \left(\frac{-7+3}{2},\frac{4+16}{2}\right)$

which equals

(-2,10) $\displaystyle (-2,10)$

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Example Question #32 : Midpoint Formula

What is the midpoint for the line segment between the points $\left ( -3,7 \right )$ $\displaystyle \left ( -3,7 \right )$ and $\left ( 5,10 \right )\ ?$ $\displaystyle \left ( 5,10 \right )\ ?$

Possible Answers:

$\left ( 4,8 \right )$ $\displaystyle \left ( 4,8 \right )$

$\left ( -4,\ -1.5 \right )$ $\displaystyle \left ( -4,\ -1.5 \right )$

$\left ( 3.5,\ 6 \right )$ $\displaystyle \left ( 3.5,\ 6 \right )$

$\left ( 1,\ 8.5 \right )$ $\displaystyle \left ( 1,\ 8.5 \right )$

$\left ( 0,8 \right )$ $\displaystyle \left ( 0,8 \right )$

Correct answer:

$\left ( 1,\ 8.5 \right )$ $\displaystyle \left ( 1,\ 8.5 \right )$

Explanation:

To find the midpoint, use the midpoint formula:

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

For this problem, this would be:

$(\frac{-3+5}{2}, \frac{7+10}{2}) = (1, 8.5)$ $\displaystyle (\frac{-3+5}{2}, \frac{7+10}{2}) = (1, 8.5)$

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Example Question #23 : How To Find The Midpoint Of A Line Segment

What is the midpoint of the line segment between points (1, 8) $\displaystyle (1, 8)$ and $\displaystyle (-7, 10)$?

Possible Answers:

(-3, 9) $\displaystyle (-3, 9)$

(-3,-9) $\displaystyle (-3,-9)$

None of the other answers are correct.

(3, -9) $\displaystyle (3, -9)$

(3,9) $\displaystyle (3,9)$

Correct answer:

(-3, 9) $\displaystyle (-3, 9)$

Explanation:

$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ $\displaystyle (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ is the midpoint formula and will give the midpoint coordinates.

Plug in the numbers from the given ordered pairs:

$(\frac{1+(-7)}{2},\frac{8+10}{2})$ $\displaystyle (\frac{1+(-7)}{2},\frac{8+10}{2})$

$(\frac{-6}{2},\frac{18}{2})$ $\displaystyle (\frac{-6}{2},\frac{18}{2})$

(-3,9) $\displaystyle (-3,9)$

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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 #851 : Functions And Lines

Example Question #852 : Functions And Lines

Example Question #853 : Functions And Lines

Example Question #1 : Midpoint Formula

Example Question #854 : Functions And Lines

Example Question #855 : Functions And Lines

Example Question #21 : How To Find The Midpoint Of A Line Segment

Example Question #22 : How To Find The Midpoint Of A Line Segment

Example Question #32 : Midpoint Formula

Example Question #23 : How To Find The Midpoint Of A Line Segment

All Algebra 1 Resources

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