   Chapter 10.1, Problem 23E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
12 views

# 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

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Expand each expression in Exercises 122. (x22x+1)2

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Find f. f(t) = t2 + 1/t2, t 0, f(2) = 3, f(1) = 2

Single Variable Calculus: Early Transcendentals, Volume I

#### The range of is: (−∞,∞) [0, ∞) (0, ∞) [1, ∞]

Study Guide for Stewart's Multivariable Calculus, 8th 