Q. 38 - 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 $5$ units.

Step 1 . Given information

The given points are $P_1(-1,0) \text{and} P_2(2,4).$

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

$$\begin{gathered} d\left(P_1,P_2\right)=\sqrt{{\left(2-(-1)\right)}^2+{\left(4-0\right)}^2} \\ =\sqrt{{\left(2+1\right)}^2+{\left(4\right)}^2} \\ =\sqrt{{\left(3\right)}^2+{\left(4\right)}^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{gathered}$$

Hence, the distance is $5$units.