what is the distance between point a and point b?

Answer:

$\sqrt{45}$

Explanation:

Step1: Identify coordinates

Let point $A=(3,3)$ and point $B=(6,9)$.

Step2: Apply 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, $x_1 = 3,y_1 = 3,x_2 = 6,y_2 = 9$. Then $d=\sqrt{(6 - 3)^2+(9 - 3)^2}$.

Step3: Calculate values inside square - root

$(6 - 3)^2=3^2 = 9$ and $(9 - 3)^2=6^2 = 36$. So, $(6 - 3)^2+(9 - 3)^2=9 + 36=45$.

Step4: Find the distance

$d=\sqrt{45}$.