Chapter 9.5, Problem 10E

To determine

Tofind:Distance between points A and C.

Answer to Problem 10E

  $d=\sqrt{18}$

Explanation of Solution

Given information:

  $\begin{array}{l}A=\left(-2,-1\right)=\left(x_1,y_1\right)\\ C=\left(1,2\right)=\left(x_2,y_2\right)\end{array}$

Concept Used:

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

Calculation:

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \Rightarrow d=\sqrt{{\left(1-\left(-2\right)\right)}^2+{\left(2-\left(-1\right)\right)}^2}\\ \Rightarrow d=\sqrt{{\left(1+2\right)}^2+{\left(2+1\right)}^2}\\ \Rightarrow d=\sqrt{{\left(3\right)}^2+{\left(3\right)}^2}\\ \Rightarrow d=\sqrt{9+9}\\ \Rightarrow d=\sqrt{18}\end{array}$