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Chapter 4: Q 274 (page 459)

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

(4,-3),(6,-4),(2,-2)

Short Answer

Expert verified

The points (4,-3),(6,-4),(2,-2) are collinear.

Step by step solution

01

Step 1. Given

The points (4,-3),(6,-4),(2,-2)

(x1,y1)=(4,-3)

(x2,y2)=(6,-4)

(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)=(4,-3),

(x2,y2)=(6,-4)

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

in the test for collinearity.

4-316-412-21=4(-4+2)-(-3)(6-2)+1(-12+8)

=4(-2)+3(4)+1(-4)

=12-12

=0

The value of determinant is zero.

So the points are collinear.

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