Question

The distance $d$from $P_1=(3,-4)$to $P_2=(-2,1)$is $d=\_\_\_\_\_\_\_\_\_\_\_$

Short answer

The distance between the points $P_1=(3,-4)$and $P_2=(-2,1)$is $5\sqrt{2}$.

Step-by-step solution

Step 1. Given Informmation

The given two points are $P_1=(3,-4)$and $P_2=(-2,1)$.

Step 2. Aim of the problem

Here, we need to find the distance between the points $P_1=(3,-4)$and $P_2=(-2,1)$

Step 3. Concept

The formula to find the distance between the points $P_1=(x_1,y_1)$and $P_2=(x_2,y_2)$is:

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Step 4. Finding the distance between the points using the distance formula

The distance between the points $P_1=(3,-4)$and $P_2=(-2,1)$is,

localid="1647084625539" $$\begin{gathered} d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2} \\ d=\sqrt{{(-2-3)}^2+(1-{(-4))}^2} \\ d=\sqrt{{(-5)}^2+{\left(5\right)}^2} \\ d=\sqrt{25+25} \\ d=\sqrt{50} \\ d=\sqrt{25\times 2} \\ d=5\sqrt{2} \end{gathered}$$

Therefore, the distance between the two given points is$5\sqrt{2}$.