Question

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
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)

Explanation:

Problem 1: Distance between (-8, -2) and (6, -1)

Step1: Identify coordinates

Let \((x_1, y_1) = (-8, -2)\) and \((x_2, y_2) = (6, -1)\).

Step2: Substitute into distance formula

\[

$$\begin{align*} d&=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\\ &=\sqrt{(6 - (-8))^2+(-1 - (-2))^2}\\ &=\sqrt{(14)^2+(1)^2}\\ &=\sqrt{196 + 1}\\ &=\sqrt{197}\\ &\approx14.04 \end{align*}$$

\]

Problem 2: Distance between (-4, 5) and (4, 0)

Step1: Identify coordinates

Let \((x_1, y_1) = (-4, 5)\) and \((x_2, y_2) = (4, 0)\).

Step2: Substitute into distance formula

\[

$$\begin{align*} d&=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\\ &=\sqrt{(4 - (-4))^2+(0 - 5)^2}\\ &=\sqrt{(8)^2+(-5)^2}\\ &=\sqrt{64 + 25}\\ &=\sqrt{89}\\ &\approx9.43 \end{align*}$$

\]

Answer:

1. The distance is approximately \(14.04\).
2. The distance is approximately \(9.43\).