Question

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

Explanation:

Step1: Recall distance formula

The distance 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

Point A: $x_1=-2,y_1=-1$; Point B: $x_2=3,y_2=2$.

Step3: Calculate differences

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

Step4: Compute squared differences

$5^2=25$, $3^2=9$.

Step5: Sum and take square root

$d=\sqrt{25+9}=\sqrt{34}$.

Answer:

$\sqrt{34}$