Q. 37 - Precalculus Enhanced with Graphing Utilities

Question

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

$P_1(3,-4) \text{and} P_2(5,4).$

Step-by-Step Solution

Answer

The distance between the given points is $2\sqrt{17}.$

Step 1 . Given information

The given points are $P_1(3,-4) \text{and} P_2(5,4).$

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

$$\begin{gathered} d\left(P_1,P_2\right)=\sqrt{{\left(5-3\right)}^2+{\left(4-(-4)\right)}^2} \\ =\sqrt{{\left(2\right)}^2+{\left(4+4\right)}^2} \\ =\sqrt{{\left(2\right)}^2+{\left(8\right)}^2} \\ =\sqrt{4+64} \\ =\sqrt{68} \\ =2\sqrt{17} \end{gathered}$$

Hence, the distance is $2\sqrt{17}$units.