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ACT Math : Lines

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Example Questions

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

What is the midpoint between (-4, -6) and (3, 7) ?

Possible Answers:

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

(1,2)

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

(1,1)

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

Correct answer:

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

Explanation:

Using the midpoint formula, $m=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

We get: $(\frac{-4+3}{2},\frac{-6+7}{2})$

Which becomes: which becomes $(-\frac{1}{2},\frac{1}{2})$

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

What is the midpoint of a line segment with endpoints (3,2) and (-1,8) ?

Possible Answers:

(11,.5)

(1,5)

(2,10)

(5,7)

(.5,11)

Correct answer:

(1,5)

Explanation:

The midpoint of a line can be found using the midpoint formula, given by:

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

Thus when we plug in our values we get the midpoint is

$\left(\frac{3+-1}{2},\frac{2+8}{2} \right )$

$=\left(\frac{2}{2},\frac{10}{2} \right )$

=(1,5)

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Example Question #14 : Midpoint Formula

What is the midpoint of the line with endpoints:

$(10,-18)\textup{ and}$ (16,8) ?

Possible Answers:

(-5,10)

(13,-5)

(-4,-13)

(80,-72)

(26,-10)

Correct answer:

(13,-5)

Explanation:

To find the midpoint given two points, use the formula:

$(\frac{x_1 +x_2}{2},\frac{y_1 +y_2}{2})$ . Thus for our points we see:

$(\frac{10+16}{2}, \frac{-18+8}{2})$ = (13,-5)

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Example Question #141 : Algebra

A line segment has endpoints at (1,-4) and (7,8) .

What is the midpoint of the line segment?

Possible Answers:

(2,-4)

(-2,-4)

(4,2)

(-4,-2)

(2,4)

Correct answer:

(4,2)

Explanation:

The midpoint can be found by using equations that calculate the values of its x- and y-coordinates. The x-coordinate can be found using the following equation:

$\frac{x_{1} + x_{2}}{2}$

Likewise, we will calculate the y-coordinate using another formula:

$\frac{y_{1} + y_{2}}{2}$

These formulas take the average of each coordinate separately in order to calculate the midpoint. In order to solve our question we will substitute in our given values and solve.

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

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

$\left (\frac{8}{2},\frac{4}{2} \right )=(4,2)$

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Example Question #142 : Algebra

A school superintendent is observing bus routes of students using a town map overlaid with a coordinate plane. Two students, Jon and Steve, live on the same street. Their houses correspond to the coordinates of (-3, 4) and (5,8), respectively, on the map. If there is a bus stop exactly between their two houses, what are the coordinates of the bus stop on the map?

Possible Answers:

(-1,11)

(0,0)

(0,5.5)

$\left(1,6\right)$

$\left(-\frac{1}{2},\frac{5}{2}\right)$

Correct answer:

$\left(1,6\right)$

Explanation:

The midpoint formula must be used to find the midpoint of the line segment joining Jon's and Steve's houses. Use the following formula to find the midpoint:

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

In this formula, $(x_{1},y_{1})$ and $(x_{2}, y_{2})$ are the coordinates of the students' homes. Substitute in the coordinates of the houses and solve for the midpoint.

$\text{Midpoint}=\left(\frac{(-3)+5}{2},\frac{4+8}{2}\right)$

$\text{Midpoint}=\left(1,6\right)$

In this case, the bus stop is at the following coordinate on the town map:

$\left(1,6\right)$

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ACT Math : Lines

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

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

Example Question #14 : Midpoint Formula

Example Question #141 : Algebra

Example Question #142 : Algebra

All ACT Math Resources

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