Geometry - How to find the midpoint of a line segment

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

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.

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

Find the midpoint of a line segment that has endpoints at and .

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

Explanation

Recall how to find the midpoint of a line segment with endpoints at and :

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

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

Find the midpoint of a line segment going from to .

Explanation

To find the midpoint of a line segment, you must find the mean of the x values and the mean of the y values.

Our x values are and to find their mean, we do .

Our y values are and , so our mean is . Therefore, our midpoint must be .

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

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

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

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

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.

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

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

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

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

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

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

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.

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

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

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

There is a line segment between the two points (5, 10) and (3, 6). What formula will give you the correct mid-point of the line segment?

$\Big( \frac{5+3}{2} ; , \frac{10+6}{2} \Big )$

$\Big( \frac{5+10}{2} ; , \frac{3+6}{2} \Big )$

$\Big( \frac{5-10}{2} ; , \frac{3-6}{2} \Big )$

$\Big( \frac{5-3}{2} ; , \frac{10-6}{2} \Big )$

$\Big( {5-2} ; ,{10-2} \Big )$

Explanation

To find the mid-point given two points on the coordinate plane you are basically finding the average of the x-values and the average of the y-values. To do this follow the formula below:

$\Big( \frac{x_{1}+ x_{2}}{2} ; , \frac{y_{1}+y_{2}}{2} \Big )$

With our points this gives:

$\Big( \frac{5+3}{2} ; , \frac{10+6}{2} \Big )$

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

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

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

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

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

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.

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

What is the midpoint of a line segment connecting the points $\left ( -5,6 \right )$ and $\left ( -3,2 \right )\ ?$

$\left ( -4,4 \right )$

$\left ( -4,2 \right )$

$\left ( -1,4 \right )$

$\left ( -1,2 \right )$

Explanation

Use the midpoint formula:

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

$(\frac{-5+(-3)}{2}, \frac{6+2}{2})=(\frac{-8}{2}, \frac{8}{2})=(-4,4)$

A line extends from the origin to $\small (14, -2)$ . What is its midpoint?

$\small (7,-1)$

$\small (7, 1 )$

$\small (1,-7)$

$\small (28, -4)$

$\small (-7, -1)$

Explanation

The origin is the point $\small (0,0)$ . We can use the regular midpoint formula with $\small (0,0)$ as $\small (x_{1}, y_{1})$ and the given point $\small (14, -2)$ as $\small (x_{2}, y_{2})$ :