Question

find the distance between the points (-6, -9) and (2, -3). write your answer as a whole number or a fully simplified radical expression. do not round. \boxed{} units

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Here, \( x_1 = -6 \), \( y_1 = -9 \), \( x_2 = 2 \), \( y_2 = -3 \).

Step2: Substitute values into formula

First, calculate \( x_2 - x_1 = 2 - (-6) = 2 + 6 = 8 \).
Then, calculate \( y_2 - y_1 = -3 - (-9) = -3 + 9 = 6 \).

Step3: Compute the distance

Now, substitute these into the distance formula:
\( d = \sqrt{(8)^2 + (6)^2} = \sqrt{64 + 36} = \sqrt{100} \).

Step4: Simplify the radical

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

Answer:

10