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((x_A+x_B)/(2),\ (y_A+y_B)/(2)\right)`

We have

`M_(AB)(10,\ 2)\\A(0,\ -2)`

Substitute:

`(0+x_B)/(2)=10\ and\ (-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)