Question

If m(10, 2) is the midpoint of the line segment ab, and if a has coordinates (0, −2), find the coordinates of
b.

Answer 1

The midpoint of the line segment AB, where

$A(x_A,\ y_A),\ B(x_B,\ y_B:)\\\\M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)$

We have

$M_{AB}(10,\ 2)\\A(0,\ -2)$

Substitute:

$\dfrac{0+x_B}{2}=10\ and\ \dfrac{-2+y_B}{2}=2\ \ \ \ |\cdot2\\\\x_B=20\ and\ -2+y_B=4\ \ \ |+2\\\\\boxed{x_B=20\ and\ y_B=6}$

Answer: B(20, 6)