   Chapter 10.3, Problem 37E 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

A B C D is a rectangle with vertex A = a ,   b in Quadrant I. The remaining vertices have symmetry with respect to A and the y -axis, A and the origin, and A and the x -axis. Find an expression for the area of A B C D in terms of a and b .

To determine

To find:

The expression for the area of ABCD in terms of a and b.

Explanation

A rectangle is drawn with the following vertices.

Aa, b in quadrant I.

The other vertices are symmetry with respect to A and the y-axis, A and the origin, and A and the x-axis.

To find the area of rectangle, find the length and breadth.

Length is AB-.

To find AB- and AD-, we have to use the distance formula.

Formula for distance between two points

d=x2-x12+y2-y12

For dAB.

x1,y1=a, b

x2,y2=-a, b

Substituting the x and y co-ordinates

dAB=-a-a2+b-b2

On solving this,

dAB=-2a2+02

dAB=4a2

dAB=2a

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