Question

find the distance between the points (-2, -9) and (5, -10). write your answer as a whole number or a fully simplified radical expression. do not round. units

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, $x_1=-2,y_1 = - 9,x_2=5,y_2=-10$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=5-(-2)=7$, and $y_2 - y_1=-10 - (-9)=-1$.

Step3: Square the differences

$(x_2 - x_1)^2=7^2 = 49$ and $(y_2 - y_1)^2=(-1)^2 = 1$.

Step4: Sum and take square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{49 + 1}=\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$

Answer:

$5\sqrt{2}$