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midpoint fun

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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