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

For \( A(-2, -1) \), \( x_1 = -2 \), \( y_1 = -1 \); for \( B(3, 2) \), \( x_2 = 3 \), \( y_2 = 2 \).

Step3: Substitute into formula

\( d = \sqrt{(3 - (-2))^2 + (2 - (-1))^2} = \sqrt{(5)^2 + (3)^2} \)

Step4: Calculate squares

\( \sqrt{25 + 9} = \sqrt{34} \)

Answer:

\(\sqrt{34}\)