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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 23 to 28, find the equation (realtionship) requested. Then eliminate fractions and square root radicals from the equation.

If A B C D , suppose that diagonals A C - and D B - are perpendicular. State an equation that relates a ,   b , and c .

To determine

To state:

An equation that relates a, b, and c for the given figure.

Explanation

The given figure is shown below.

It is given that AC- and DB- are perpendicular.

Hence, the product of their slopes is -1.

That is mAC·mDB=-1

Finding the slope of AC.

x1,y1=A0, 0

x2,y2=Ca+b, c

Formula for slope of the line containing two points.

Slope is denoted by m.

m=y2-y1x2-x1

Here x1x2

Substituting the x and y co-ordinates.

mAC=c-0a+b-0

Simplifying,

mAC=ca+b

Finding the slope of DB.

x1,y1=Db, c

x2,y2=Ba, 0

Substituting the x and y co-ordinates

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