Q. 41 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

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

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 $\sqrt{53}$.