Proof of the Midpoint Formula Let P and Q be the points (x1, y1) and (x2, y2), respectivel...

Proof of the Midpoint Formula Let P and Q be the points (x1, y1) and (x2, y2), respectively, and let M be the point with coordinates

Use the distance formula to compute the following:

(a) The distance d from P to Q;

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(b) The distance d1 from M to P;

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(c) The distance d2 from M to Q.

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(d) Verify that d1 = d2.

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(e) Show that d1 + d2 = d. [Hint: Verify that and .]

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(f) Explain why parts (d) and (e) show that M is the midpoint of PQ.