Question

The midpoint of AB is (1, 2). The coordinates of A are (-3,6).Find the coordinates of B.

Answer 1

Midpoint has coordinates $(x_m,y_m)$ which equal to,

$x_m=\frac{x_1+x_2}{2}$

$y_m=\frac{y_1+y_2}{2}$

We know the coordinates of a midpoint as well as the coordinates of $A(x_1,y_1)$ so we should be able to find coordinates of $B(x_2,y_2)$.

First solve both equations for $x_2$ and $y_2$ respectively,

$x_2=2x_m-x_1$

$y_2=2y_m-y_1$

Now insert the data,

$x_2=2\cdot1-(-3)=\boxed{5}$

$y_2=2\cdot2-6=\boxed{-2}$

The coordinates of B are therefore $(5,-2)$.

Hope this helps :)