   Chapter 10.3, Problem 7E 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

In Exercises 5 to 10, the real numbers a, b, c, and d are positive.Consider the quadrilateral with vertices at M 0 ,   0 , N a ,   0 , P a + b ,   c , and Q b ,   c . Explain why M N P Q is a parallelogram. To determine

To explain:

MNPQ is a parallelogram.

Explanation

The given diagram is shown below.

To prove MNPQ is a parallelogram, we have to prove the following statement.

Both pairs of opposite sides are parallel.

MN is parallel to QP.

That is slope of MN is equal to slope of PQ.

Also, QM is parallel to PN.

That is slope of QM is equal to slope of PN.

Find the slope of MN.

x1,y1=M0, 0

x2,y2=Na, 0

Formula for slope joining the line segment.

Slope is denoted by m.

m=y2-y1x2-x1

Here x1x2

Substituting the x and y co-ordinates.

mMN=0-0a-0

mMN=0

Then, find the slope of QP.

x1,y1=Qb, c

x2,y2=Pa+b, c

Substituting the x and y co-ordinates.

mQP=c-ca+b-b

mQP=0a

mQP=0

mMN=mQP

Hence, MN and QP are parallel

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