Chapter 1, Problem 1RE

(a)

To determine

To find: find the distance between the points.

Answer to Problem 1RE

Therefore, the distance between the two points is $2\sqrt{5}$ units.

Explanation of Solution

Given:

Given points are $(0,0);(4,2)$

Calculation:

The distance between two points, $P_1=\left(x_1,y_1\right)$ and $P_2=\left(x_2,y_2\right)$ is,

  $d\left(P_1,P_2\right)=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Substitute the values of $x_1,x_2,y_1,$ and $y_2$

  $\begin{array}{ll}{P}_2=(4,2)\hfill & \hfill \\ d\left(P_1,P_2\right)\hfill & =\sqrt{{(4-0)}^2+{(2-0)}^2}\hfill \\ \hfill & =\sqrt{16+4}\hfill \\ \hfill & =\sqrt{20}\hfill \\ \hfill & =2\sqrt{5}\hfill \end{array}$

Therefore, the distance between the two points is $2\sqrt{5}$ units.

Conclusion:

Therefore, the distance between the two points is $2\sqrt{5}$ units.