Question

what is the length of $overline{ab}$? round your answer to the nearest hundredth.

Explanation:

Step1: Identify coordinates

Assume each grid - square is 1 unit. Point A has coordinates (-5, - 4) and point B has coordinates (-3, 3).

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, $x_1=-5,y_1 = - 4,x_2=-3,y_2 = 3$. Then $d=\sqrt{(-3-(-5))^2+(3 - (-4))^2}=\sqrt{(2)^2+(7)^2}$.

Step3: Calculate value

$\sqrt{(2)^2+(7)^2}=\sqrt{4 + 49}=\sqrt{53}\approx7.28$.

Answer:

$7.28$