Chapter 9.3, Problem 2MRE

a.

To determine

To find: The slope of PQ.

Answer to Problem 2MRE

The slope of PQ is 4.

Explanation of Solution

Given information: The coordinates of points: $P\left(1,-6\right)$ and $Q\left(3,2\right)$ .

Formula used: $Slope=\frac{y_2-y_1}{x_2-x_1}$

Calculation: Apply the slope formula to calculate the slope of the given line PQ.

  $\begin{array}{l}=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{2-\left(-6\right)}{3-1}\\ =\frac{8}{2}\\ =4\end{array}$

Therefore, the required slope is 4.

b.

To determine

To find: The distance of PQ.

Answer to Problem 2MRE

The distance of PQ is $2\sqrt{17}$ .

Explanation of Solution

Given information: The coordinates of points: $P\left(1,-6\right)$ and $Q\left(3,2\right)$ .

Formula used: $D=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Calculation: Apply the distance formula to calculate the distance of the given line PQ.

  $\begin{array}{l}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(3-1\right)}^2+{\left(2+6\right)}^2}\\ =\sqrt{2^2+8^2}\\ =\sqrt{68}\\ =2\sqrt{17}\end{array}$

Therefore, the required distance is $2\sqrt{17}$ .

c.

To determine

To find: The midpoint of PQ.

Answer to Problem 2MRE

The midpoint of PQ is $\left(2,-2\right)$ .

Explanation of Solution

Given information: The coordinates of points: $P\left(1,-6\right)$ and $Q\left(3,2\right)$ .

Formula used: $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Calculation: Apply the midpoint formula to calculate the midpoint of PQ.

  $\begin{array}{l}M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{1+3}{2},\frac{-6+2}{2}\right)\\ =\left(2,-2\right)\end{array}$

Therefore, the required midpoint is $\left(2,-2\right)$ .