Question

find the distance between the two points.

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, $(x_1,y_1)=(-3,-4)$ and $(x_2,y_2)=(2,2)$.

Step2: Calculate differences

$x_2 - x_1=2-(-3)=5$ and $y_2 - y_1=2 - (-4)=6$.

Step3: Square the differences

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=6^2 = 36$.

Step4: Sum and square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{25 + 36}=\sqrt{61}$.

Answer:

$\sqrt{61}$