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Chapter 4: Q 272 (page 459)

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

(0,1),(2,0),(-2,2)

Short Answer

Expert verified

The points (0,1),(2,0),(-2,2) are collinear.

Step by step solution

01

Step 1. Given

The points (0,1),(2,0),(-2,2)

(x1,y1)=(0,1)

(x2,y2)=(2,0)

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

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)=(0,1),

(x2,y2)=(2,0)

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

in the test for collinearity.

011201-221=0(0-2)-1(2+2)+1(4-0)

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

=-4+4

=0

The value of determinant is zero.

So the points are collinear.

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