Question

The distance $d$from $P_1=(2,-5)$to $P_2=(4,-2)$is $d=\_\_\_\_\_\_\_\_$.

Short answer

The distance$d$from$P_1=(2,-5)to{P}_2=(4,-2)$isrole="math" localid="1646794105762" $d=\mathbf{3}\mathbf{.}\mathbf{61}\mathbf{}\mathbf{.}$

Step-by-step solution

Step 1. Given Information

Given Points:

$P_1=(2,-5)to{P}_2=(4,-2)$.

We have to find the distance between two given points .

Step 2. Solution:

Using distance formula:

$$\begin{gathered} d(P_1,P_2)=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2} \\ ForDis\tan ce{P}_1(x_1,y_1)to{P}_2(x_2,y_2) \end{gathered}$$

We have

$$\begin{gathered} d(P_1,P_2)=\sqrt{{(4-2)}^2+(-2-{(-5))}^2} \\ d(P_1,P_2)=\sqrt{{\left(2\right)}^2+{\left(3\right)}^2} \\ d(P_1,P_2)=\sqrt{4+9} \\ d(P_1,P_2)=\sqrt{13} \\ d(P_1,P_2)\approx 3.61 \end{gathered}$$