Question

find the distance between each pair of points. round to the nearest hundredth.

1. (-8, -2) and (6, -1)
2. (-4, 5) and (4, 0)

12 _

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Solve for points $(-8,-2)$ and $(6,-1)$

For $(x_1,y_1)=(-8,-2)$ and $(x_2,y_2)=(6,-1)$:
\[

$$\begin{align*} d&=\sqrt{(6-(-8))^2+((-1)-(-2))^2}\\ &=\sqrt{(6 + 8)^2+(-1 + 2)^2}\\ &=\sqrt{14^2+1^2}\\ &=\sqrt{196 + 1}\\ &=\sqrt{197}\\ &\approx14.04 \end{align*}$$

\]

Step3: Solve for points $(-4,5)$ and $(4,0)$

For $(x_1,y_1)=(-4,5)$ and $(x_2,y_2)=(4,0)$:
\[

$$\begin{align*} d&=\sqrt{(4-(-4))^2+(0 - 5)^2}\\ &=\sqrt{(4 + 4)^2+(0-5)^2}\\ &=\sqrt{8^2+(-5)^2}\\ &=\sqrt{64+25}\\ &=\sqrt{89}\\ &\approx9.43 \end{align*}$$

\]

Answer:

1. Approximately $14.04$
2. Approximately $9.43$