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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 $k$?

 Apr 12, 2018
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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  )

 Apr 12, 2018

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