   Chapter 10.2, Problem 25E 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

Find x such that the points A x ,   5 , B 2 ,   3 , and C 4 ,   - 5 are collinear.

To determine

To find:

The value of x for the collinear points Ax, 5, B2, 3, and C4, -5.

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 x2x1

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

The given points are Ax, 5, and B2, 3.

Using the slope formula and choosing x1=x, x2=2, y1=5, and y2=3.

mAB-=3-52-x

mAB-=-22-x

The given points are B2, 3 and C4, -5

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