Q. 36 - 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 $\sqrt{10}.$

Step 1 . Given information

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

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

$$\begin{gathered} d\left(P_1,P_2\right)=\sqrt{{\left(2-(-1)\right)}^2+{\left(2-1\right)}^2} \\ =\sqrt{{\left(2+1\right)}^2+{\left(2-1\right)}^2} \\ =\sqrt{{\left(3\right)}^2+{\left(1\right)}^2} \\ =\sqrt{9+1} \\ =\sqrt{10} \end{gathered}$$

Hence, the distance is $\sqrt{10}$units.