Question

what is the distance between point a(-2, -1) and point b(3, 2)?

Explanation:

Step1: Recall Distance Formula

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

Step2: Identify Coordinates

Let \( A(-2, -1) \) be \((x_1, y_1)\) and \( B(3, 2) \) be \((x_2, y_2)\).

Step3: Substitute into Formula

Calculate \( x_2 - x_1 = 3 - (-2) = 5 \) and \( y_2 - y_1 = 2 - (-1) = 3 \).
Then \( d = \sqrt{(5)^2 + (3)^2} = \sqrt{25 + 9} = \sqrt{34} \).

Answer:

\(\sqrt{34}\)