Chapter B, Problem 1E

To determine

The distance between the points $\left(1,1\right)\text{ and }\left(4,5\right)$ .

Answer to Problem 1E

The distance between the points $\left(1,1\right)\text{ and }\left(4,5\right)$ is $5\text{units}$ .

Explanation of Solution

Given:

The given points are $\left(1,1\right)\text{ and }\left(4,5\right)$ .

Formula used:

If $\left|d\right|$ is the distance between the points $\left(x_1,y_1\right)\text{ and }\left(x_2,y_2\right)$ then $\left|d\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\mathrm{....}\left(1\right)$

Calculation:

With the help of formula (1) stated above the distance $\left|d\right|$ between the points $\left(1,1\right)\text{ and }\left(4,5\right)$ is evaluated as:

  $\begin{array}{c}\left|d\right|=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(4-1\right)}^2+{\left(5-1\right)}^2}\\ =\sqrt{3^2+4^2}\\ =\sqrt{5^2}\\ =5\text{units}\end{array}$

Hence, the distance between the points $\left(1,1\right)\text{ and }\left(4,5\right)$ is $5\text{units}$ .