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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 10.CR, Problem 13CR
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Elementary Geometry for College St...

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

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Find x so that - 2 ,   3 , x ,   6 , and 8 ,   8 are collinear.

To determine

To find:

The value of x for the collinear points -2, 3, x, 6, and 8, 8.

Explanation

If the points are collinear, then the slope of the lines making with the points are same.

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 the given points be A-2, 3, Bx, 6, and C8, 8.

Let mAB- and mBC- are the slopes of the line AB- and BC- respectively.

The slope of the line AB- A-2, 3, and Bx, 6 is obtained below.

Using the slope formula and choosing x1=-2, x2=x, y1=3, and y2=6.

mAB-=6-3x--2

mAB-=3x+2

The slope of the line BC- Bx, 6, and C8, 8 is obtained below

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