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Chapter 4: Q 396 (page 483)

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

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

Short Answer

Expert verified

The points (0,2),(-1,-1),(-2,4) are not collinear.

Step by step solution

01

Step 1. Given Information

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

(x1,y1)=(0,2)

(x2,y2)=(-1,-1)

(x3,y3)=(-2,4)

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 in the formula

Substitute the points (x1,y1)=(0,2), (x2,y2)=(-1,-1)(x3,y3)=(-2,4)in the formula.


x1y11x2y21x3y31=021-1-11-241

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

=0-2(1)+1(-6)

=-2-6

=-8

The value of the determinant is non zero number.

So, the points are not collinear.

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