Chapter 1, Problem 3RE

(a)

To determine

To find: find the distance between the points.

Answer to Problem 3RE

The distance between the two points is 5 units.

Explanation of Solution

Given:

Given points are $(1,-1);(-2,3)$

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 $y_2$

  $d\left(P_1,P_2\right)=\sqrt{{(3-(-1))}^2+{(-2-1)}^2}=\sqrt{16+9}=\sqrt{25}=5$

Therefore, the distance between the two points is 5 units.

Conclusion:

Therefore, the distance between the two points is 5 units.