Math CentralQuandaries & Queries


Question from sefora, a student:

The coordinates of the vertices of quadrilaterals are given.
Draw each quadrilateral on a grid.
Determine whether it is a rectangle (show your work)

P(5,1), Q(-4,4), R(-6,-2), S(3,-5)


Let me try 4 different points

A(3,2), B(-1,-2), C(-2,4), D(4,-3)

Here is my sketch


I plotted the four points and them to form 4 line segments with no internal crossings. It sure doesn't look like a rectangle. If it were a rectangle then the adjacent sides BD and DA would be perpendicular. I'll check by calculating the slopes

Slope of BD: [-3 - (-2)]/[4 - (-1)] = -1/5
Slope of DA: [2 - (-3)]/[3 - 4] = 5/-1 = -5

If these line segments were perpendicular then slope DA = -1/[Slope BD], but this is not true so ACBD is not a rectangle.

I hope this helps,

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