Chapter 9.5, Problem 62E

To determine

Tofind:Distance between given points.

Answer to Problem 62E

  $d=5\sqrt{2}$

Explanation of Solution

Given information:

  $\begin{array}{l}A\left(x_1,y_1\right)=A\left(-2,3\right)\\ B\left(x_2,y_2\right)=B\left(3,-2\right)\end{array}$

Concept Used:

Distance between two points - $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Calculation:

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \Rightarrow d=\sqrt{{\left(3-\left(-2\right)\right)}^2+{\left(-2-3\right)}^2}\\ \Rightarrow d=\sqrt{{\left(5\right)}^2+{\left(-5\right)}^2}\\ \Rightarrow d=\sqrt{25+25}\\ \Rightarrow d=\sqrt{50}\\ \Rightarrow d=5\sqrt{2}\end{array}$

Option D is correct