Chapter 8, Problem 1T

Find the distance between the points $(-3,5)$ and (2, 1).

To determine

To calculate:

The distance between the points $\left(-3,5\right)$ and $\left(2,1\right)$.

Answer to Problem 1T

Solution:

The distance between the points $\left(-3,5\right)$ and $\left(2,1\right)$ is $\underset{\_}{\sqrt{41}}$.

Explanation of Solution

Given:

The two distinct points, $\left(-3,5\right)$ and $\left(2,1\right)$.

Formula Used:

The distance between two points can be calculated by:

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

Calculation:

Let the two points are:

$\left(x_1,y_1\right)=\left(-3,5\right)$

And,

$\left(x_2,y_2\right)=\left(2,1\right)$

Since, it is known that the distance between two points can be given by distance formula:

$\begin{array}{ccc}\hfill d& =& \sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\hfill \\ \hfill & =& \sqrt{{\left(2-\left(-3\right)\right)}^2+{\left(1-5\right)}^2}\hfill \\ \hfill & =& \sqrt{{\left(5\right)}^2+{\left(-4\right)}^2}\hfill \\ \hfill & =& \sqrt{25+16}\hfill \end{array}$

i.e.., $d=\sqrt{41}$

Hence, the distance between two points will be $\underset{\_}{\sqrt{41}}$.