Chapter 1.1, Problem 23AYU

To determine

The distance between the given points

Answer to Problem 23AYU

  $d\left(P_1,P_2\right)=20\text{units}$

Explanation of Solution

Given:

The given points are

  $\begin{array}{l}{P}_1=\left(-3,2\right)\\ P_2=\left(6,0\right)\end{array}$

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

  $\begin{array}{l}d\left(P_1,P_2\right)=\sqrt{{\left(11-\left(-5\right)\right)}^2+{\left(9-\left(-3\right)\right)}^2}\\ d\left(P_1,P_2\right)=\sqrt{{\left(16\right)}^2+{\left(12\right)}^2}\\ d\left(P_1,P_2\right)=\sqrt{256+144}\\ d\left(P_1,P_2\right)=\sqrt{400}\\ d\left(P_1,P_2\right)=20\text{units}\end{array}$