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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 10.2, Problem 42E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Find an equation involving a , b , c , d , and e if A C ⃡ ⊥ B C ⃡ .

(HINT: Use slopes.)

Chapter 10.2, Problem 42E, Find an equation involving a, b, c, d, and e if ACBC. HINT: Use slopes.

To determine

To find:

An equation involving a, b, c, d, and e if AC⃡⊥BC⃡.

Elementary Geometry for College Students, Chapter 10.2, Problem 42E

Explanation

By theorem,

If two lines are perpendicular, then the product of their slopes is -1 or one slope is negative reciprocal of the other slope.

(i.e) If l1⊥l2, then m1.m2=-1 or m2=-1m1

Here AC⃡⊥BC⃡, thus we have to find the slopes for the two lines AC⃡ and BC⃡.

Then by using the theorem, we can make the required equation.

The slope of the line that contains the points x1,y1 and x2,y2 is given by

m=y2-y1x2-x1 for x2≠x1

Let mAC- and mBC- are the slopes of the line AC- and BC- respectively.

The given vertices are Aa, b, and Cc, d.

Using the slope formula and choosing x1=a, x2=c, y1=b, and y2=d.

mAC-=d-bc-a

The given vertices are Be, b and Cc, d

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