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Intermediate Geometry : Coordinate Geometry

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Example Questions

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Example Question #11 : Midpoint Formula

A line segment has endpoints (8, 1) and (2, 5). What is the midpoint of this segment?

Possible Answers:

$(\frac{13}{2}, \frac{1}{2})$

(5, 3)

(5, 1)

(3, 12)

Correct answer:

(5, 3)

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{8+2}{2}, \frac{1+5}{2})=(5, 3)$

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Example Question #12 : Midpoint Formula

A line segment has endpoints at (10, 2) and (-10, -6). What is the midpoint of this line?

Possible Answers:

(8, 1)

(0, -4)

(-2, 2)

(0, -2)

Correct answer:

(0, -2)

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{10-10}{2}, \frac{2-6}{2})=(0, -2)$

Report an Error

Example Question #13 : Midpoint Formula

A line segments has endpoints at (-5, 1) and (-2, 9). What is the midpoint of this line segment?

Possible Answers:

(3, 1)

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

$(\frac{9}{2}, 2)$

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

Correct answer:

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

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{-5-2}{2}, \frac{1+9}{2})=(-\frac{7}{2}, 5)$

Report an Error

Example Question #14 : Midpoint Formula

Find the midpoint of a line that has endpoints at (9, 2) and (11, 6).

Possible Answers:

(15, 13)

(20, 8)

(10, 4)

(13, 2)

Correct answer:

(10, 4)

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{9+11}{2}, \frac{2+6}{2})=(10, 4)$

Report an Error

Example Question #15 : Midpoint Formula

Find the midpoint of a line that has endpoints at (-15, 2) and (-2, 2).

Possible Answers:

$(-\frac{17}{2}, 2)$

(-12, 2)

$(-\frac{13}{2},2)$

$(-\frac{15}{2}, -2)$

Correct answer:

$(-\frac{17}{2}, 2)$

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{-15-2}{2}, \frac{2+2}{2})=(-\frac{17}{2}, 2)$

Report an Error

Example Question #16 : Midpoint Formula

Find the midpoint of a line segment that has endpoints at (-9,-1) and (1,2).

Possible Answers:

$(-\frac{11}{2}, 0)$

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

$(-4, \frac{1}{2})$

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

Correct answer:

$(-4, \frac{1}{2})$

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{-9+1}{2}, \frac{-1+2}{2})=(-4, \frac{1}{2})$

Report an Error

Example Question #17 : Midpoint Formula

Find the midpoint of a line segment with endpoints at (10, 2) and (-2, -8).

Possible Answers:

(-9, 2)

(3, 4)

(1, 2)

(4, -3)

Correct answer:

(4, -3)

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{10-2}{2}, \frac{2-8}{2})=(4, -3)$

Report an Error

Example Question #18 : Midpoint Formula

Find the midpoint of a line segment that has endpoints at (5,1) and (-3, -10).

Possible Answers:

$(1, -\frac{9}{2})$

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

$(-\frac{11}{2}, 2)$

$(4, \frac{9}{2})$

Correct answer:

$(1, -\frac{9}{2})$

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{5-3}{2}, \frac{1-10}{2})=(1, -\frac{9}{2})$

Report an Error

Example Question #19 : Midpoint Formula

Find the midpoint of a line segment that has endpoints at (0.6, 9) and (-9.2, 7).

Possible Answers:

(-4.3, 8)

(-4.2, 0)

(-4.9, 1)

(-4.8, -2)

Correct answer:

(-4.3, 8)

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{0.6-9.2}{2}, \frac{9+7}{2})=(-4.3, 8)$

Report an Error

Example Question #20 : Midpoint Formula

Find the midpoint of a line segment that has endpoints at (12, 12) and (-10, 24).

Possible Answers:

(11, 13)

(2, 12)

(1, 18)

(13, 4)

Correct answer:

(1, 18)

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{12-10}{2}, \frac{12+24}{2})=(1,18)$

Report an Error

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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #11 : Midpoint Formula

Example Question #12 : Midpoint Formula

Example Question #13 : Midpoint Formula

Example Question #14 : Midpoint Formula

Example Question #15 : Midpoint Formula

Example Question #16 : Midpoint Formula

Example Question #17 : Midpoint Formula

Example Question #18 : Midpoint Formula

Example Question #19 : Midpoint Formula

Example Question #20 : Midpoint Formula

All Intermediate Geometry Resources

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