   Chapter 10.1, Problem 23E 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 rectangle ABCD has three of its vertices at A ( 2 ,   - 1 ) ,   B ( 6 ,   - 1 ) , and C ( 6 ,   3 ) . Find the fourth vertex and the area of the rectangle ABCD.

To determine

To find:

The fourth vertex and the area of the rectangle ABCD. The other three vertices of the rectangle is A(2, -1), B(6, -1), and C(6, 3).

Explanation

Three vertices of the rectangle ABCD is A(2, -1), B(6, -1), and C(6, 3).

Let Fourth vertex of the rectangle D=x, y.

AB is horizontal side of rectangle, since y values of A and B are same =-1.

BC is vertical side of the rectangle, since x values of C and B are same =6.

Hence, AD must be another vertical side and CD is the another horizontal side of the rectangle.

D has same as the x coordinate of A and has same as the y coordinate of C.

Hence, the coordinates of D=(2, 3)

Plotting the four coordinates A(2, -1), B(6, -1), and C6, 3, D(2, 3) in the graph as shown below,

Length of AB and BC can be determined using distance formula,

Distance Formula:

The distance between the two points (x1, y1) and (x2, y2) as below,

d=(x2-x1

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