Question

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

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

Short answer

The distance between the points is $d=\sqrt{53}$.

Step-by-step solution

Step 1. Given information.

Find the distance between the points.

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

Step 2. Substitute the values in the formula.

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

$$\begin{gathered} d=\sqrt{{\left(x_2-x_1\right)}^2+{(y_2-y_2)}^2} \\ d=\sqrt{{\left(6-4\right)}^2+{(4-(-3\left)\right)}^2} \\ d=\sqrt{{\left(2\right)}^2+{\left(7\right)}^2} \\ d=\sqrt{4+49} \\ d=\sqrt{53} \end{gathered}$$

Step 3. Conclusion.

The distance between the points is$\sqrt{53}$.