Q.39 - Precalculus Enhanced with Graphing Utilities

Question

Find the distance $d(P_1,P_2)$between the points $P_1$ and $P_2.$

Step-by-Step Solution

Answer

The distance between the given points is $20$ units.

Step 1 . Given information

The given points are $P_1(-5,-3) \text{and} P_2(11,9).$

Step 2 . Formula used

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

Step 3 . Find the distance

$$\begin{gathered} d\left(P_1,P_2\right)=\sqrt{{\left(11-(-5)\right)}^2+{\left(9-(-3)\right)}^2} \\ =\sqrt{{\left(11+5\right)}^2+{\left(9+3\right)}^2} \\ =\sqrt{{\left(16\right)}^2+{\left(12\right)}^2} \\ =\sqrt{400} \\ =20 \end{gathered}$$

Hence, the distance is $20$units.