Question

if $overline{ab}$ has endpoints at $a(-3, -3)$ and $b(5, 3)$, what is its length? use the keypad to enter the answer in the box provided. $ab=square$ units.

Explanation:

Step1: Identify the 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, $x_1=-3,y_1 = - 3,x_2=5,y_2 = 3$.

Step2: Substitute the values into the formula

$AB=\sqrt{(5-(-3))^2+(3 - (-3))^2}=\sqrt{(5 + 3)^2+(3 + 3)^2}=\sqrt{8^2+6^2}$.

Step3: Calculate the squares and sum

$\sqrt{8^2+6^2}=\sqrt{64 + 36}=\sqrt{100}$.

Step4: Find the square - root

$\sqrt{100}=10$.

Answer:

$10$