Question

If m(8, 1) is the midpoint of the line segment ab, and if a has coordinates (6, −2), find the coordinates of

b.

Answer 1

The formula of a midpoint:

`M\left((x_1+x_2)/(2);\ (y_2-y_1)/(2)\right)`

We have:

`(6,\ -2)\to x_1=6,\ y_1=-2\\\\M(8,\ 1)`

Substitute:

`(6+x_2)/(2)=8\ and\ (-2+y_2)/(2)=1`

First equation:

`(6+x_2)/(2)=8\ \ \ |\cdot2\\\\6+x_2=16\ \ \ |-6\\\\x_2=10`

Second equation:

`(-2+y_2)/(2)=1\ \ \ \ |\cdot2\\\\-2+y_2=2\ \ \ |+2\\\\y_2=4`

Answer: The coordinates of point B are (10, 4).