# How do you find the coordinates of the other endpoint of a segment with the given endpoint of a segment is (12, -8) and the midpoint is (3, 18)?

Jun 22, 2016

The other end is at $\left(- 6 , 44\right)$

#### Explanation:

The vector displacement from $\left(12 , - 8\right)$ to $\left(3 , 18\right)$ is
$\textcolor{w h i t e}{\text{XXX")vec(""(3-12,18-(-8)))= vec(} \left(- 9 , 26\right)}$

A point twice as far away from $\left(12 , 8\right)$ (but through $\left(3 , 18\right)$
would have a vector displacement of
$\textcolor{w h i t e}{\text{XXX")2xxvec(""(-9,26))=vec(} \left(- 18 , 52\right)}$
from $\left(12 , - 8\right)$

(12,-8)+vec(""(-18,52))=(-6,44)