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What is the slope of the line containing the midpoint of the segment with endpoints at $(2, 4)$ and $(0, -2)$ and the midpoint of the segment with endpoints at $(5, 1)$ and $(1, 5)?$ Express your answer in simplest form.

 Jun 23, 2020
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Using the midpoint formula, we find that the midpoint of the first segment is

\((\frac{2+0}{2}, \frac{4-2}{2})\)=\((\frac{2}{2}, \frac{2}{2})\)=\((1, 1)\)

 

The midpoint of the second segment is 

\((\frac{5+1}{2}, \frac{1+5}{2})\)=\((\frac{6}{2}, \frac{6}{2})\)=\((3, 3)\).

 

Using the slope formula, we find that the slope of the line with points \((1, 1)\) and \((3, 3)\) is:

\(\frac{3-1}{3-1}=\frac{2}{2}=1\)

 Jun 23, 2020

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