Chapter 1, Problem 6RE

(a)

To determine

To find: the distance between the points.

Answer to Problem 6RE

The distance between the two points is 5 units.

Explanation of Solution

Given:

Given points are (-3,4) $;(2,4)$

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

  $d\left(P_1,P_2\right),$ is

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

Substitute $x_1=-3,x_2=2,y_1=4,y_2=4$ in the formula and evaluate.

  $\begin{array}{l}\begin{array}{l}d\left(P_1,P_2\right)=\sqrt{{[2-(-3)]}^2+{(4-4)}^2}\\ =\sqrt{25+0}\end{array}\hfill \\ =5\hfill \end{array}$

The distance between the two points is 5 units.

Conclusion:

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