Chapter 9.3, Problem 1ST

To determine

To calculate: The distance between the pairs of points.

Answer to Problem 1ST

The distance between the given points is $\sqrt{65}$ .

Explanation of Solution

Given information: The coordinates of points are $\left(3,-6\right)$ and $\left(4,2\right)$ .

Formula used: $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Calculation: Apply the distance formula to calculate the distance between the two points.

  $\begin{array}{cc}A& B\\ x_1=3& x_2=4\\ y_1=-6& y_2=2\end{array}$

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ d=\sqrt{{\left(4-3\right)}^2+{\left(2-\left(-6\right)\right)}^2}\\ d=\sqrt{1+64}\\ d=\sqrt{65}\end{array}$

Therefore, the required distance between the points is $\sqrt{65}$ .