Q. 21 - Geometry

Question

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)

Step-by-Step Solution

Answer

We have proved that the points $P,Q\text{ and }R$ are collinear.

Step-1 – Given

The given points are$P\left(-8,6\right),Q\left(-5,5\right)\text{ and }R\left(4,2\right)$ .

Step-2 – To determine

We have to show that points $P,Q\text{ and }R$ are collinear by showing that$\overline{PQ}$ and$\overline{QR}$ 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 $P\left(-8,6\right),Q\left(-5,5\right)\text{ and }R\left(4,2\right)$

Slope of $\overline{PQ}$:

$\frac{y_2-y_1}{x_2-x_1}=\frac{5-6}{-5-\left(-8\right)}=\frac{-1}{3}=-0.34$

Slope of $\overline{QR}$:

$\frac{y_2-y_1}{x_2-x_1}=\frac{2-5}{4-\left(-5\right)}=\frac{-3}{9}=-0.34$

Since, the slope of $\overline{PQ}$and $\overline{QR}$are equal, so the points$P,Q\text{ and }R$ are collinear.