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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

The midpoint formula is

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

So for our two points the equation is

$\displaystyle \left(\frac{0+2}{2},\frac{4+8}{2}\right)$

$\displaystyle \left(\frac{2}{2},\frac{12}{2}\right)$

$\displaystyle (1,6)$

The midpoint formula is

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

If we plug in our points we get

$\displaystyle \left(\frac{0+3}{2},\frac{0+4}{2}\right)$

$\displaystyle \left(\frac{3}{2},\frac{4}{2}\right)$

$\displaystyle (1.5,2)$

The midpoint formula is

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

So lets plug in our two points, that gives us

$\displaystyle \left(\frac{1+3}{2},\frac{9+5}{2}\right)$

$\displaystyle \left(\frac{4}{2},\frac{14}{2}\right)$

$\displaystyle (2,7)$

The equation to find the midpoint between two points is

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

If we plug in our values of the two points we get

$\displaystyle \left(\frac{0+4}{2},\frac{0+5}{2}\right)$

$\displaystyle \left(\frac{4}{2},\frac{5}{2}\right)$

$\displaystyle (2,2.5)$

The midpoint's coordinates are the average of the endpoints'.

This means that the x-coordinates of the two endpoints have a mean of 1:

$\displaystyle \small \frac{8+x }{2} = 1$ multiply both sides by 2

$\displaystyle \small 8 + x = 2$ subtract 8

$\displaystyle \small x = -6$ this means the other endpoint's x-coordinate is -6

This also means that the y-coordinates of the two endpoints have a mean of -3:

$\displaystyle \small \frac{-7+y}{2} = -3$ multiply both sides by 2

$\displaystyle \small -7 + y = -6$ add 7 to both sides

$\displaystyle \small y = 1$

The coordinate pair that we're looking for is (-6, 1)

The midpoint's coordinates are just the mean of the endpoints'.

This means that the mean of the two x-coordinates is 9:

$\displaystyle \small \frac{x+ 1}{2} = 9$ multiply both sides by 2

$\displaystyle \small x + 1 = 18$ subtract 1

$\displaystyle \small x = 17$

This also means that the mean of the two y-coordinates is 9:

$\displaystyle \small \frac{y+17}{2} = 9$ multiply both sides by 2

$\displaystyle \small y + 17 = 18$ subtract 17

$\displaystyle \small y = 1$

So the other endpoint we were solving for is $\displaystyle \small (17, 1 )$