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Chapter 4: Q 275 (page 459)

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

(-2,1),(-4,4),(0,-2)

Short Answer

Expert verified

The points (-2,1),(-4,4),(0,-2) are collinear

Step by step solution

01

Step 1. Given

The points (-2,1),(-4,4),(0,-2)

(x1,y1)=(-2,1)

(x2,y2)=(-4,4)

(x3,y3)=(0,-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)=(-2,1),

(x2,y2)=(-4,4)d

(x3,y3)=(0,-2)

in the test for collinearity.

-211-4410-21=-2(4+2)-1(-4+0)+1(8-0)

=-2(6)-1(-4)+1(8)

=-12+12

=0

The value of determinant is zero.

So the points are collinear.

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