   Chapter 10.1, Problem 24E 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 M N P Q has three of its vertices at M ( 0, 0 ) ,   N ( a ,   0 ) , and Q ( 0 ,   b ) . Find the fourth vertex P and the area of the rectangle M N P Q .

To determine

To find:

The fourth vertex P and the area of the rectangle MNPQ. The other three vertices of the rectangle is M(0, 0), N(a, 0), and Q(0, b).

Explanation

Three vertices of the rectangle MNPQ is M(0, 0), N(a, 0), and Q(0, b).

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

MN is horizontal side of rectangle, since y values of M and N are same =0.

MQ is vertical side of the rectangle, since x values of M and Q are same =0.

Hence, NP must be another vertical side and QP is the another horizontal side of the rectangle.

P has same as the x coordinate of N and has same as the y coordinate of Q.

Hence, the coordinates of P=(a,b)

Sketch the four coordinates M(0, 0), N(a, 0), and Q(0, b), P(a,b) in the graph as shown below,

Length of MN and MQ 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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