Q. 42 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

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

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 $5\sqrt{5}$.