Question

The points W, left parenthesis, 5, comma, minus, 3, right parenthesis, comma, X, left parenthesis, minus, 1, comma, 9, right parenthesis, comma, Y, left parenthesis, minus, 5, comma, 7, right parenthesisW(5,−3),X(−1,9),Y(−5,7), and Z, left parenthesis, 1, comma, minus, 5, right parenthesisZ(1,−5) form quadrilateral WXYZ. Plot the points then click the "Graph Quadrilateral" button., On this question page, you will first graph points on a coordinate grid. Following the graph are two buttons, "Graph Quadrilateral" will drawn lines between your points, and "Reset" will remove all of your points. Once you press Graph Quadrilateral, if your points are correct, the answer area will appear.
Click on the graph to plot a point. Click a point to delete it.
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W
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Use the dropdown menus and answer blanks below to prove the quadrilateral is a rectangle.
Answer
Attempt 1 out of 2

I will prove that quadrilateral WXYZ is a rectangle by demonstrating that
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Answer 1

I will prove that quadrilateral WXYZ is a rectangle by demonstrating that it is a parallelogram and one angle is a right angle (so it must be a rectangle).

Compute slopes of the sides:
- slope WX = (9 − (−3)) / (−1 − 5) = 12 / (−6) = −2
- slope XY = (7 − 9) / (−5 − (−1)) = −2 / (−4) = 1/2
- slope YZ = (−5 − 7) / (1 − (−5)) = −12 / 6 = −2
- slope ZW = (−3 − (−5)) / (5 − 1) = 2 / 4 = 1/2

Since slope WX = slope YZ and slope XY = slope ZW, both pairs of opposite sides are parallel → WXYZ is a parallelogram.

Also slope WX · slope XY = (−2)·(1/2) = −1, so WX is perpendicular to XY → one interior angle is a right angle.

A parallelogram with a right angle is a rectangle. Therefore WXYZ is a rectangle.