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

Question

Accepted Answer

# Explanation:
## Step1: Identify the coordinates of the two points
From the graph, the first point (let's say $ P $) has coordinates $ (-7, -3) $ and the second point (let's say $ Q $) has coordinates $ (-3, -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 = -7 $, $ y_1 = -3 $, $ x_2 = -3 $, and $ y_2 = -5 $ into the formula:

$$
\begin{align*}
d&=\sqrt{(-3 - (-7))^2 + (-5 - (-3))^2}\
&=\sqrt{(-3 + 7)^2 + (-5 + 3)^2}\
&=\sqrt{(4)^2 + (-2)^2}\
&=\sqrt{16 + 4}\
&=\sqrt{20}\
&=\sqrt{4\times5}\
&= 2\sqrt{5}
\end{align*}
$$

# Answer:
$ 2\sqrt{5} $

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the coordinates of the two points

Step2: Apply the distance formula

Answer: