Chapter 9.5, Problem 7E

To determine

Tofind:Distance between points A and B.

Answer to Problem 7E

  $d=\sqrt{17}$

Explanation of Solution

Given information:

  $\begin{array}{l}A=\left(-2,-1\right)=\left(x_1,y_1\right)\\ B=\left(-1,3\right)=\left(x_2,y_2\right)\end{array}$

Concept Used:

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

Calculation:

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ \Rightarrow d=\sqrt{{\left(-1-\left(-2\right)\right)}^2+{\left(3-\left(-1\right)\right)}^2}\\ \Rightarrow d=\sqrt{{\left(-1+2\right)}^2+{\left(3+1\right)}^2}\\ \Rightarrow d=\sqrt{{\left(1\right)}^2+{\left(4\right)}^2}\\ \Rightarrow d=\sqrt{1+16}\\ \Rightarrow d=\sqrt{17}\end{array}$