what is the distance between (-13, 9) and (11, 2) on a coordinate grid?

Answer

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, $x_1=-13,y_1 = 9,x_2=11,y_2 = 2$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=11-(-13)=11 + 13=24$, $y_2 - y_1=2 - 9=-7$.

Step3: Square the differences

$(x_2 - x_1)^2=24^2 = 576$, $(y_2 - y_1)^2=(-7)^2=49$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=576 + 49=625$.

Step5: Take the square - root

$d=\sqrt{625}=25$.