Question

find the distance between the two points in simplest radical form.

Explanation:

Step1: Identify the coordinates of the two points.

Looking at the graph, the first point (let's call it \( P_1 \)) is at \( (-2, 3) \) and the second point ( \( P_2 \)) is at \( (-8, -5) \).

Step2: Apply the distance formula.

The distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Substitute \( x_1 = -2 \), \( y_1 = 3 \), \( x_2 = -8 \), \( y_2 = -5 \) into the formula:
\[

$$\begin{align*} d &= \sqrt{(-8 - (-2))^2 + (-5 - 3)^2}\\ &= \sqrt{(-8 + 2)^2 + (-8)^2}\\ &= \sqrt{(-6)^2 + 64}\\ &= \sqrt{36 + 64}\\ &= \sqrt{100} \end{align*}$$

\]

Step3: Simplify the radical.

\( \sqrt{100} = 10 \).

Answer:

10