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Chapter 4: Q 273 (page 459)

In the following exercises, determine whether the given points are collinear.

(0,-5),(-2,-2),(2,-8)

Short Answer

Expert verified

The points (0,-5),(-2,-2),(2,-8) are collinear.

Step by step solution

01

Step 1. Given

The points (0,-5),(-2,-2),(2,-8)

(x1,y1)=(0,-5)

(x2,y2)=(-2,-2)

(x3,y3)=(2,-8)

To find if the points are collinear.

02

Step 2. Test for collinear points

Three points(x1,y1),(x2,y2),(x3,y3) are collinear if and only if x1y11x2y21x3y31=0

03

Step 3. Substitute the points

Substitute the points (x1,y1)=(0,-5),

(x2,y2)=(-2,-2)

(x3,y3)=(2,-8)

in the test for collinearity.

0-51-2-212-81=0(-2+8)-(-5)(-2-2)+1(16+4)

=0+5(-4)+1(20)

=-20+20

=0

The value of determinant is zero.

So the points are collinear.

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