Chapter 1.1, Problem 21AYU

To determine

The distance between the given points

Answer to Problem 21AYU

  $d\left(P_1,P_2\right)=2\sqrt{17}\text{ units}$

Explanation of Solution

Given:

The given points are

  $\begin{array}{l}{P}_1=\left(3,-4\right)\\ P_2=\left(5,4\right)\end{array}$

Calculation:

The distance between two points $P_1=\left(x_1,y_1\right)\text{and }{P}_2=\left(x_2,y_2\right)$ can be calculated as

  $d\left(P_1,P_2\right)=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

The distance can be calculated as

  $\begin{array}{l}d\left(P_1,P_2\right)=\sqrt{{\left(5-3\right)}^2+{\left(4-\left(-4\right)\right)}^2}\\ d\left(P_1,P_2\right)=\sqrt{{\left(2\right)}^2+{\left(8\right)}^2}\\ d\left(P_1,P_2\right)=\sqrt{4+64}\\ d\left(P_1,P_2\right)=\sqrt{68}\\ d\left(P_1,P_2\right)=\sqrt{4\cdot 17}\\ d\left(P_1,P_2\right)=2\sqrt{17}\text{ units}\end{array}$