Question

find the distance d(a,b) between points a and b. a(3,3); b(-2,-1) d(a,b)= (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 3,y_1 = 3,x_2=-2,y_2=-1$.

Step2: Substitute values

$d(A,B)=\sqrt{(-2 - 3)^2+(-1 - 3)^2}=\sqrt{(-5)^2+(-4)^2}$.

Step3: Calculate squares

$\sqrt{(-5)^2+(-4)^2}=\sqrt{25 + 16}$.

Step4: Simplify

$\sqrt{25+16}=\sqrt{41}$.

Answer:

$\sqrt{41}$