Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 10 - Section 10.5 - Equations of Lines - Exercises - Page 472: 43

Answer

$(b, \frac{ab-b^2}{c})$

Work Step by Step

We first describe the slope. Using the knowledge of the point we are looking for, we see that the equation of the line is: $ y=\frac{a-b}{c}x$ We find the slope of one of the lines is: c/b Since this is perpendicular to the other line being considered, we find that the slope of that line is: -b/c (a,0) is on this line, which means the equation of the line can be described as: $y=-b/c(x-a)$ We equate these two equations to have: $\frac{a-b}{c}x=-b/c(x-a)$ Upon solving, we find: x =b We substitute back into the equation to find y: $ y = \frac{ab-b^2}{c}$ This gives the point: $(b, \frac{ab-b^2}{c})$
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