   Chapter 10.2, Problem 16E 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

Are these points collinear?a) A - 1 ,   - 2 , B 3 ,   2 , and C 5 ,   5 b) D a ,   c - d , E b ,   c , and F 2 b - a ,   c + d

To determine

(a)

To check:

Whether the points A-1, -2, B3, 2, and C5, 5 are collinear.

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 A-1, -2 and B3, 2.

Using the slope formula and choosing x1=-1, x2=3, y1=-2, and y2=2

To determine

(b)

To check:

Whether the points Da, c-d, Eb, c, and F2b-a, c+d are collinear.

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