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

Explanation:

Step1: Identify distance - formula

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

Step2: Assign values

Let $(x_1,y_1)=(-2,-1)$ and $(x_2,y_2)=(3,2)$. Then $x_2 - x_1=3-(-2)=5$ and $y_2 - y_1=2 - (-1)=3$.

Step3: Calculate distance

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

Answer:

$\sqrt{34}$