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

Step 1. Given

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

$(x_{1}, y_{1}) = (4, - 3)$

$(x_{2}, y_{2}) = (6, - 4)$

$(x_{3}, y_{3}) = (2, - 2)$

To find if the points are collinear.

Step 2. Test for collinear points

Three points $(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})$ are collinear if and only if $|\begin{matrix} x_{1} & y_{1} & 1 \\ x_{2} & y_{2} & 1 \\ x_{3} & y_{3} & 1 \end{matrix}| = 0$

Step 3. Substitute the points

Substitute the points $(x_{1}, y_{1}) = (4, - 3)$ ,

$(x_{2}, y_{2}) = (6, - 4)$

$(x_{3}, y_{3}) = (2, - 2)$

in the test for collinearity.

$|\begin{matrix} 4 & - 3 & 1 \\ 6 & - 4 & 1 \\ 2 & - 2 & 1 \end{matrix}| = 4 (- 4 + 2) - (- 3) (6 - 2) + 1 (- 12 + 8)$

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

$= 12 - 12$

$= 0$

The value of determinant is zero.

So the points are collinear.

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In the following exercises, determine whether the given points are collinear.
$(4, - 3), (6, - 4), (2, - 2)$

Short Answer

Step by step solution

Step 1. Given

Step 2. Test for collinear points

Step 3. Substitute the points

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In the following exercises, determine whether the given points are collinear.(4,-3),(6,-4),(2,-2)

Short Answer

Step by step solution

Step 1. Given

Step 2. Test for collinear points

Step 3. Substitute the points

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Mechanics Maths

Statistics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, determine whether the given points are collinear.
$(4, - 3), (6, - 4), (2, - 2)$