Chapter 1, Problem 4RE

(a)

To determine

To find: find the distance between the points.

Answer to Problem 4RE

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

Explanation of Solution

Given:

Given points are $(-2,2);(1,4)$

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

  $\begin{array}{l}d\left(P_1,P_2\right),\text{ is }\hfill \\ d\left(P_1,P_2\right)=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\hfill \end{array}$

Substitute $x_1=-2,x_2=1,y_1=2,y_2=4$ in the formula and evaluate.

  $d\left(P_1,P_2\right)=\sqrt{{[1-(-2)]}^2+{(4-2)}^2}=\sqrt{9+4}=\sqrt{13}$

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

Conclusion:

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