Question

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

Short answer

The distance between the given points is$\sqrt{10}.$

Step-by-step solution

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

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

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