How to find the midpoint of a line segment - SSAT Upper Level Quantitative

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Question

A line segment on the coordinate plane has endpoints and . In terms of and , as applicable, give the -coordinate of its midpoint.

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Answer

The -coordinate of the midpoint of a line segment is the mean of the -coordinates of its endpoints. Therefore, the -coordinate is

$y= $\frac{(a-4)+(-b)}{2}$ = $\frac{a-b-4}{2}$$ .

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Question

A line segment on the coordinate plane has endpoints and . In terms of and , as applicable, give the -coordinate of its midpoint.

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Answer

The -coordinate of the midpoint of a line segment is the mean of the -coordinates of its endpoints. Therefore, the -coordinate is

$x= $\frac{(a-5)+(b+8)}{2}$ = $\frac{a+b-5+8}{2}$ = $\frac{a+b+3}{2}$$ .

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Question

A line segment has the endpoints and . What is the midpoint of the line?

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Answer

To find the midpoint of a line, take the averages of the x-coordinates and the average of the y-coordinates.

$$\text{Midpoint}$=($\frac{6+(-2)}{2}$, $\frac{10+(-4)}{2}$)=($\frac{4}{2}$, $\frac{6}{2}$)=(2,3)$

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Question

What is the midpoint of a line segment with endpoints and ?

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Answer

To find the midpoint of a line, just take the average of the -coordinates and the average of the -coordinates.

$$\text{Midpoint}$=($\frac{12+(-2)}{2}$, $\frac{2+1}{2}$)=($\frac{10}{2}$, $\frac{3}{2}$)=(5, $\frac{3}{2}$)$

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Question

What is the midpoint of a line segments with endpoints and ?

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Answer

To find the midpoint of a line segment, take the average of the -coordinates, then take the average of the -coordinates.

$$\text{Midpoint}$=($\frac{2a+4a}{2}$, $\frac{-b+5b}{2}$)$

$$\text{Midpoint}$=($\frac{6a}{2}$, $\frac{4b}{2}$)=(3a, 2b)$

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Question

A line has the endpoints $(8,8) $\text{ and }$(2, -1)$ . What is its midpoint?

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Answer

The coordinates of the midpoint of a line are just the averages of the coordinates of the endpoints.

$$\text{Midpoint}$=\left($\frac{8+2}{2}$, $\frac{8-1}{2}\right)=\left(5, $\frac{7}{2}\right)$

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Question

A line segment has endpoints $(-2, 0) $\text{ and }$(1, 5)$ . What is the midpoint of this line segment?

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Answer

To find the coordinates of the midpoint of a line, take the averages of the x and y coordinates of the endpoints.

$$\text{Midpoint}$=\left($\frac{-2+1}{2}$, $\frac{5+0}{2}\right)=\left(-$\frac{1}{2}$, $\frac{5}{2}\right)$

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Question

What is the midpoint of a line if the endpoints of the line are: $(6,9) \textup{ and }(3,-2)$ ?

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Answer

Write the midpoint formula.

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

Substitute the values.

$M=\left($\frac{6+3}{2}$,$\frac{9-2}{2}\right)= \left($\frac{9}{2}$,$\frac{7}{2}\right)$

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Question

A line segment on the coordinate plane has endpoints and . In terms of and , as applicable, give the -coordinate of its midpoint.

Tap to reveal answer

Answer

The -coordinate of the midpoint of a line segment is the mean of the -coordinates of its endpoints. Therefore, the -coordinate is

$y= $\frac{(a-4)+(-b)}{2}$ = $\frac{a-b-4}{2}$$ .

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Question

A line segment on the coordinate plane has endpoints and . In terms of and , as applicable, give the -coordinate of its midpoint.

Tap to reveal answer

Answer

The -coordinate of the midpoint of a line segment is the mean of the -coordinates of its endpoints. Therefore, the -coordinate is

$x= $\frac{(a-5)+(b+8)}{2}$ = $\frac{a+b-5+8}{2}$ = $\frac{a+b+3}{2}$$ .

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Question

A line segment has the endpoints and . What is the midpoint of the line?

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Answer

To find the midpoint of a line, take the averages of the x-coordinates and the average of the y-coordinates.

$$\text{Midpoint}$=($\frac{6+(-2)}{2}$, $\frac{10+(-4)}{2}$)=($\frac{4}{2}$, $\frac{6}{2}$)=(2,3)$

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Question

What is the midpoint of a line segment with endpoints and ?

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Answer

To find the midpoint of a line, just take the average of the -coordinates and the average of the -coordinates.

$$\text{Midpoint}$=($\frac{12+(-2)}{2}$, $\frac{2+1}{2}$)=($\frac{10}{2}$, $\frac{3}{2}$)=(5, $\frac{3}{2}$)$

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Question

What is the midpoint of a line segments with endpoints and ?

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Answer

To find the midpoint of a line segment, take the average of the -coordinates, then take the average of the -coordinates.

$$\text{Midpoint}$=($\frac{2a+4a}{2}$, $\frac{-b+5b}{2}$)$

$$\text{Midpoint}$=($\frac{6a}{2}$, $\frac{4b}{2}$)=(3a, 2b)$

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Question

A line has the endpoints $(8,8) $\text{ and }$(2, -1)$ . What is its midpoint?

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Answer

The coordinates of the midpoint of a line are just the averages of the coordinates of the endpoints.

$$\text{Midpoint}$=\left($\frac{8+2}{2}$, $\frac{8-1}{2}\right)=\left(5, $\frac{7}{2}\right)$

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Question

A line segment has endpoints $(-2, 0) $\text{ and }$(1, 5)$ . What is the midpoint of this line segment?

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Answer

To find the coordinates of the midpoint of a line, take the averages of the x and y coordinates of the endpoints.

$$\text{Midpoint}$=\left($\frac{-2+1}{2}$, $\frac{5+0}{2}\right)=\left(-$\frac{1}{2}$, $\frac{5}{2}\right)$

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Question

What is the midpoint of a line if the endpoints of the line are: $(6,9) \textup{ and }(3,-2)$ ?

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Answer

Write the midpoint formula.

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

Substitute the values.

$M=\left($\frac{6+3}{2}$,$\frac{9-2}{2}\right)= \left($\frac{9}{2}$,$\frac{7}{2}\right)$

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Question

A line segment has the endpoints and . What is the midpoint of the line?

Tap to reveal answer

Answer

To find the midpoint of a line, take the averages of the x-coordinates and the average of the y-coordinates.

$$\text{Midpoint}$=($\frac{6+(-2)}{2}$, $\frac{10+(-4)}{2}$)=($\frac{4}{2}$, $\frac{6}{2}$)=(2,3)$

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Question

A line segment on the coordinate plane has endpoints and . In terms of and , as applicable, give the -coordinate of its midpoint.

Tap to reveal answer

Answer

The -coordinate of the midpoint of a line segment is the mean of the -coordinates of its endpoints. Therefore, the -coordinate is

$y= $\frac{(a-4)+(-b)}{2}$ = $\frac{a-b-4}{2}$$ .

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Question

A line segment on the coordinate plane has endpoints and . In terms of and , as applicable, give the -coordinate of its midpoint.

Tap to reveal answer

Answer

The -coordinate of the midpoint of a line segment is the mean of the -coordinates of its endpoints. Therefore, the -coordinate is

$x= $\frac{(a-5)+(b+8)}{2}$ = $\frac{a+b-5+8}{2}$ = $\frac{a+b+3}{2}$$ .

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Question

What is the midpoint of a line segment with endpoints and ?

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Answer

To find the midpoint of a line, just take the average of the -coordinates and the average of the -coordinates.

$$\text{Midpoint}$=($\frac{12+(-2)}{2}$, $\frac{2+1}{2}$)=($\frac{10}{2}$, $\frac{3}{2}$)=(5, $\frac{3}{2}$)$

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