   Chapter 10.CR, Problem 33CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Prove the statements in Review Exercises 32 to 36 using analytic geometry.If the diagonals of a rectangle are perpendicular, then the rectangle is a square.

To determine

The analytic proof for the given theorem “If the diagonals of a rectangle are perpendicular, then the rectangle is a square.”

Explanation

Given theorem is,

If the diagonals of a rectangle are perpendicular, then the rectangle is a square.

The above figure shows the rectangle ABCD.

The coordinates of the rectangle is A0, 0, Ba, 0, C(a, b) and D(0, b).

The diagonals AC and BD are joined as shown in the figure.

If ab, these points are form a rectangle.

If a=b, these points are form a square.

Condition for diagonal to be perpendicular is,

m1·m2=-1

Let m1 be the slope of the diagonal AC.

And let m2 be the slope of the diagonal BD

Formula for slope of the line is m=y2-y1x2-x1

x1, y1=(0, 0)

x2, y2=(a, b

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