Question

Given A(-3, 8), find the coordinates of the point B such that C(5, -8) is the midpoint of segment AB.

Answer 1

We know that the coordinates of the midpoint are the average of the coordinates of the two endpoints.

So, we have

$C_x = \dfrac{A_x+B_x}{2},\quad C_y=\dfrac{A_y+B_y}{2}$

Plug the known values for A and C and solve each equation for the coordinates of point B:

$5 = \dfrac{-3+B_x}{2},\quad -8=\dfrac{8+B_y}{2}$

Multiply both equations by 2:

$10 = -3+B_x,\quad -8=8+B_y$

Subtract the known coordinate from each equation:

$13 = B_x,\quad -16=B_y$

So, the point B is $(13,-16)$