   Chapter 10.4, Problem 21E 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

Use slopes to verify that the graphs of the questions A x + B y = C and B x - A y = D are perpendicular.(Note: A ≠ 0   a n d   B ≠ 0 . )

To determine

To verify:

The graph of the equations Ax+By=C and Bx-Ay=D are perpendicular using slopes.

Explanation

The given equations are,

Ax+By=C

And Bx-Ay=D

Formula for finding the slope:

y=mx+c

Here, m is the slope.

For the equation Ax+By=C

Subtracting Ax on both sides of the equation,

Ax-Ax+By=C-Ax

By=C-Ax

Dividing the above equation by B,

y=C-AxB

y=-ABx+CB

Where, m1=-AB

Similarly, for the equation Bx-Ay=D

Subtracting Bx on both sides of the equation,

Bx-Bx-Ay=D-Bx

-Ay=D</

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