Chapter 13: Q. 21 (page 533)

In Exercises 20 and 21 show that points P, Q, and R are collinear by showing that PQ and OR have the same slope.
P(-8, 6) Q(-5, 5) R(4, 2)

Short Answer

Expert verified

We have proved that the points $P, Q and R$ are collinear.

Step by step solution

Step-1 – Given

The given points are $P (- 8, 6), Q (- 5, 5) and R (4, 2)$ .

Step-2 – To determine

We have to show that points $P, Q and R$ are collinear by showing that $\bar{P Q}$ and $\bar{Q R}$ have the same slope.

Step-3 – Calculation

We’ll use the slope formula:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

The given points are $P (- 8, 6), Q (- 5, 5) and R (4, 2)$

Slope of $\bar{P Q}$ :

$\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{5 - 6}{- 5 - (- 8)} = \frac{- 1}{3} = - 0.34$

Slope of $\bar{Q R}$ :

$\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{2 - 5}{4 - (- 5)} = \frac{- 3}{9} = - 0.34$

Since, the slope of $\bar{P Q}$ and $\bar{Q R}$ are equal, so the points $P, Q and R$ are collinear.

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In Exercises 20 and 21 show that points P, Q, and R are collinear by showing that PQ and OR have the same slope.
P(-8, 6) Q(-5, 5) R(4, 2)

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

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In Exercises 20 and 21 show that points P, Q, and R are collinear by showing that PQ and OR have the same slope.P(-8, 6) Q(-5, 5) R(4, 2)

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

In Exercises 20 and 21 show that points P, Q, and R are collinear by showing that PQ and OR have the same slope.
P(-8, 6) Q(-5, 5) R(4, 2)