Chapter 9.1, Problem 9OE

To determine

To calculate: The distance between the pair of points.

Answer to Problem 9OE

The distance between the given points is $\sqrt{10}$ .

Explanation of Solution

Given information: The coordinates of two points are $\left(3,1\right)$ and $\left(2,4\right)$ .

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

Calculation:

Let the two given points be $A\left(3,1\right),B\left(2,4\right)$ and distance between points be AB.

So,

  $\begin{array}{cc}A& B\\ x_1=3& x_2=2\\ y_1=1& y_2=4\end{array}$

Put the value of x and y coordinates into the formula.

  $\begin{array}{l}AB=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ AB=\sqrt{{\left(2-3\right)}^2+{\left(4-1\right)}^2}\\ AB=\sqrt{1+9}\\ \therefore AB=\sqrt{10}\end{array}$

Thus, the distance between the two points is $\sqrt{10}$ .