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 say \( (x_1, y_1) \)) is at \( (2, -9) \) and the second point \( (x_2, y_2) \) is at \( (4, -4) \).

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 \( x_1 = 2 \), \( y_1 = -9 \), \( x_2 = 4 \), \( y_2 = -4 \) into the formula:

First, calculate \( x_2 - x_1 = 4 - 2 = 2 \).

Then, calculate \( y_2 - y_1 = -4 - (-9) = -4 + 9 = 5 \).

Now, substitute these values into the distance formula:

\( d = \sqrt{(2)^2 + (5)^2} \)

Step3: Simplify the expression.

Calculate \( (2)^2 = 4 \) and \( (5)^2 = 25 \).

Then, \( 4 + 25 = 29 \).

So, \( d = \sqrt{29} \).

Answer:

\(\sqrt{29}\)