Question

Find the distance from $P_1$to$P_2$.
role="math" localid="1646776682625" $P_1=(2,-3,-3)and{P}_2=(4,1,-1)$

Short answer

The distance between points$P_1=(2,-3,-3)and{P}_2=(4,1,-1)$is$2\sqrt{6}$

Step-by-step solution

Step 1. Given data

The given points are

$$\begin{gathered} P_1(x_1,y_1,z_1)=(2,-3,-3) \\ {P}_2(x_2,y_2,z_2)=(4,1,-1) \end{gathered}$$

Step 2. Distance between points

Use distance formula

$$\begin{gathered} d(P_1,P_2)=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2} \\ d(P_1,P_2)=\sqrt{{\left(4-2\right)}^2+{\left(1-\left(-3\right)\right)}^2+{\left(-1-\left(-3\right)\right)}^2} \\ d(P_1,P_2)=\sqrt{4+16+4} \\ d(P_1,P_2)=\sqrt{24} \\ d(P_1,P_2)=2\sqrt{6} \end{gathered}$$

so the distance between points is$2\sqrt{6}$