Chapter 1, Problem 2RE

(a)

To determine

To find: find the distance between the points.

Answer to Problem 2RE

The distance between the two points is $2\sqrt{13}$ units.

Explanation of Solution

Given:

Given points are $(0,0);(-4,6)$

Calculation:

For any two points $P_1\left(x_1,y_1\right)$ and $P_2\left(x_2,y_2\right)$ . the distance between the two points, denoted by $d\left(P_1,P_2\right),$ is

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

Substitute $x_1=0,x_2=-4,y_1=0,y_2=6$

  $d\left(P_1,P_2\right)=\sqrt{{(-4-0)}^2+{(6-0)}^2}=\sqrt{16+36}=\sqrt{52}=2\sqrt{13}$

The distance between the two points is $2\sqrt{13}$ units.

Conclusion:

The distance between the two points is $2\sqrt{13}$ units.