Question

find the distance between the points (-9, 8) and (-1, -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, $x_1=-9,y_1 = 8,x_2=-1,y_2=-10$.

Step2: Calculate differences

$x_2 - x_1=-1-(-9)=-1 + 9=8$ and $y_2 - y_1=-10 - 8=-18$.

Step3: Square the differences

$(x_2 - x_1)^2=8^2 = 64$ and $(y_2 - y_1)^2=(-18)^2=324$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=64 + 324=388$.

Step5: Take square - root

$d=\sqrt{388}=\sqrt{4\times97}=2\sqrt{97}$.

Answer:

$2\sqrt{97}$