The four points $A(-4,0), B(0,-4), X(0,8),$ and $Y(14,k)$ are grouped on the Cartesian plane. If segment $AB$ is parallel to segment $XY$ what is the value of $k$?

gueesstt Apr 12, 2018

#1**+1 **

The four points A(-4,0) , B(0,-4) , X(0,8) , and Y(14,k) are grouped on the Cartesian plane.

If segment AB is parallel to segment XY, then...

the slope of AB = the slope of XY

\(\frac{-4-0}{0--4}\,=\,\frac{k-8}{14-0}\\~\\ \frac{-4}{4}\,=\,\frac{k-8}{14}\\~\\ -1\,=\,\frac{k-8}{14}\\~\\ -1\cdot14\,=\,k-8\\~\\ -14\,=\,k-8\\~\\ -14+8\,=\,k\\~\\ -6\,=\,k\)

( Here's a graph to check this: https://www.desmos.com/calculator/864gc7gxq2 )

hectictar Apr 12, 2018