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Intermediate Geometry : How to find the midpoint of a line segment

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Example Question #21 : Coordinate Geometry

Find the midpoint of a line segment that has endpoints at $\left(\frac{1}{2}, 5\right)$ and $\left(-\frac{3}{2}, 1\right)$ .

Possible Answers:

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

$(-\frac{3}{4}, 6)$

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

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

Correct answer:

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

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.

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

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Example Question #22 : Coordinate Geometry

Find the midpoint of a line segment that has endpoints at (9, 120) and (-24, 2) .

Possible Answers:

$(-\frac{15}{2}, 61)$

$(\frac{15}{2}, 61)$

$(-\frac{15}{2}, 59)$

$(-\frac{33}{2}, 60)$

Correct answer:

$(-\frac{15}{2}, 61)$

Explanation:

Recall how to find the midpoint of a line segment with endpoints at (x_1, y_1) and (x_2, y_2) :

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

$\text{Midpoint}=(\frac{9+(-24)}{2}, \frac{120+2}{2})=(-\frac{15}{2}, 61)$

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Example Question #23 : Coordinate Geometry

Find the midpoint of a line segment that has endpoints at (16, 7) and (8, 9) .

Possible Answers:

(12, 8)

(4, -1)

(1, 8)

$(\frac{25}{2}, \frac{15}{2})$

Correct answer:

(12, 8)

Explanation:

Recall how to find the midpoint of a line segment with endpoints at (x_1, y_1) and (x_2, y_2) :

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

$\text{Midpoint}=(\frac{16+8}{2}, \frac{7+9}{2})=(12, 8)$

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Example Question #24 : Coordinate Geometry

A line segment on the coordinate plane has its endpoints at (3.8, -1.7) and (9.2, 5.5) .

True or false: Its midpoint is located at (6.5, 3.6) .

Possible Answers:

False

True

Correct answer:

False

Explanation:

The midpoint of a line segment with endpoints $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is located at $\left ( \frac{x_{1}+x_{2}}{2} , \frac{y_{1}+ y_{2}}{2} \right )$ .

Set $x_{1}= 3.8, y_{1} =-1.7,x_{2} =9.2, y_{2}= 5.5$ , and evaluate both expressions:

$\frac{x_{1}+x_{2}}{2}= \frac{3.8+9.2}{2} = \frac{13}{2} = 6.5$

$\frac{-1.7+5.5}{2} =\frac{3.8}{2} = 1.9$

The midpoint is at (6.5, 1.9) , so the statement is false.

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Intermediate Geometry : How to find the midpoint of a line segment

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #21 : Coordinate Geometry

Example Question #22 : Coordinate Geometry

Example Question #23 : Coordinate Geometry

Example Question #24 : Coordinate Geometry

All Intermediate Geometry Resources

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