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Algebra 1 : Functions and Lines

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Example Questions

Example Question #1 : How To Find The Midpoint Of A Line Segment

Find the midpoint that falls between (1,-7) and (13,3) .

Possible Answers:

(7,-2)

(14,-4)

(5,1)

(-7,2)

(-2,7)

Correct answer:

(7,-2)

Explanation:

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

When we plug in our points, we get $\left ( \frac{14}{2}, \frac{-4}{2}\right)$ .

So, our final answer is (7,-2) .

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Example Question #2 : How To Find The Midpoint Of A Line Segment

A line is drawn from (2,4) to (8,28). What are the coordinates of its midpoint?

Possible Answers:

$\left ( 5,20 \right )$

$\left ( 5,16 \right )$

$\left ( 3,12 \right )$

$\left ( 4,14 \right )$

Correct answer:

$\left ( 5,16 \right )$

Explanation:

The length to the midpoint is the difference between the two points divided by two. That number must then be added to the point:

$X_{midpoint}=X_{1}+\frac{\left (X_{2}-X_{1} \right )}{2}=2+\frac{\left (8-2 \right )}{2}=2+\frac{6}{2}=2+3=5$

$Y_{midpoint}=Y_{1}+\frac{\left (Y_{2}-Y_{1} \right )}{2}=4+\frac{\left (28-4 \right )}{2}=4+\frac{24}{2}=4+12=16$

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Example Question #7 : How To Find The Midpoint Of A Line Segment

A line segment begins at (2,3) and ends at the point (16,11) . What is the location of its midpoint?

Possible Answers:

(9,7)

(5,6)

(14,8)

(7,4)

(9,8)

Correct answer:

(9,7)

Explanation:

The difference in -values is 14 and the difference in -values is 8. The midpoint therefore differs by values of 7 and 4 from either of the endpoints.

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Example Question #3 : How To Find The Midpoint Of A Line Segment

$\textup{Two points }S\left ( 5,2\right )\textup{ and }T\left ( -3,10\right )\textup{ lie in the }xy\textup{-coordinate plane.}$

$\textup{What is the midpoint of line segment }\overline{ST}\textup{ ?}$

Possible Answers:

$\left ( 2,8\right )$

$\left ( 1,10\right )$

$\left (5,6\right )$

$\left ( 4,6\right )$

$\left ( 1,6\right )$

Correct answer:

$\left ( 1,6\right )$

Explanation:

$\textup{The coordinates of the midpoint are the averages of the other points' coordinates.}$

$x\textup{-coordinate}=\frac{5+\left ( -3)\right )}{2}=1\;\;\;\;y\textup{-coordinate}=\frac{2+10}{2}=6$

$\textup{The midpoint is at }\left (1,6\right )$

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Example Question #9 : How To Find The Midpoint Of A Line Segment

A line has endpoints of (5,-2) and (-1,0) . What is its midpoint?

Possible Answers:

(3,-1)

(1,1)

(2,1)

(2,-1)

(2,-2)

Correct answer:

(2,-1)

Explanation:

The midpoint formula is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

To find the midpoint of (5,-2) and (-1,0) , you simply plug in the points into the midpoint formula: $(\frac{5+-1}{2},\frac{-2+0}{2})$ , which gives you the point (2,-1) .

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Example Question #10 : How To Find The Midpoint Of A Line Segment

A line has endpoints of $\left ( 10,-2 \right )$ and $\left ( -4,8 \right )$ . What is its midpoint?

Possible Answers:

(-7,-6)

None of the other answers

(3,3)

(7,6)

(-3,-3)

Correct answer:

(3,3)

Explanation:

You can find the midpoint of the line by using the midpoint formula: $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ . Plug the endpoints into the formula to get $(\frac{10+-4}{2},\frac{{-2}+8}{2})$ , or (3,3) .

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Example Question #12 : Midpoint Formula

What is the midpoint of a line with endpoints of (-10,14) and (4,2) ?

Possible Answers:

(-3,8)

(-7,-6)

(7,6)

None of the other answers

(3,-8)

Correct answer:

(-3,8)

Explanation:

To find the midpoint, use the midpoint formula: $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$ . Plug in the two ordered pairs to the formula to get: $(\frac{-10+4}{2},\frac{14+2}{2})$ . Doing this will give you a solution of (-3,8) .

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Example Question #841 : Functions And 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 IV

Quadrant II

The -axis

Quadrant III

Quadrant I

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 #841 : Functions And Lines

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

Possible Answers:

Quadrant III

Quadrant II

The -axis

Quadrant I

Quadrant IV

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 #843 : Functions And Lines

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

Possible Answers:

(-8, 8)

(-4, 4)

(-5, 4)

(-2, 4)

(4, -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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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Find The Midpoint Of A Line Segment

Example Question #2 : How To Find The Midpoint Of A Line Segment

Example Question #7 : How To Find The Midpoint Of A Line Segment

Example Question #3 : How To Find The Midpoint Of A Line Segment

Example Question #9 : How To Find The Midpoint Of A Line Segment

Example Question #10 : How To Find The Midpoint Of A Line Segment

Example Question #12 : Midpoint Formula

Example Question #841 : Functions And Lines

Example Question #841 : Functions And Lines

Example Question #843 : Functions And Lines

All Algebra 1 Resources

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