Question

Find the distance $d(P_1,P_2)$between the points $P_1\mathrm{and}{P}_2$.

$P_1=(-4,-3);P_2=(6,2)$

Short answer

The distance between the points is$d=5\sqrt{5}$.

Step-by-step solution

Step 1. Given information.

Find the distance between the points.
$P_1=(-4,-3);P_2=(6,2)$

Step 2. Substitute the values in the formula.

The length of the line segment is the distance between the points $P_1=(x_1,y_1)=(-4,-3)\mathrm{and}{P}_2=(x_2,y_2)=(6,2)$. Using the distance formula with$x_1=-4,y_1=-3,x_2=6,\mathrm{and}{y}_2=2$, the length d is

$$\begin{gathered} d=\sqrt{{\left(x_2-x_1\right)}^2+{(y_2-y_2)}^2} \\ d=\sqrt{{\left(6-(-4)\right)}^2+{(2-(-3\left)\right)}^2} \\ d=\sqrt{{\left(10\right)}^2+{\left(5\right)}^2} \\ d=\sqrt{100+25} \\ d=\sqrt{125} \\ d=5\sqrt{5} \end{gathered}$$

Step 3. Conclusion.

The distance between the points is$5\sqrt{5}$.