Question

find the distance between the points (-4, 10) and (-5, -3). 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, $x_1=-4,y_1 = 10,x_2=-5,y_2=-3$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-5-(-4)=-5 + 4=-1$ and $y_2 - y_1=-3 - 10=-13$.

Step3: Square the differences

$(x_2 - x_1)^2=(-1)^2 = 1$ and $(y_2 - y_1)^2=(-13)^2 = 169$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=1 + 169=170$.

Step5: Find the square - root

$d=\sqrt{170}$

Answer:

$\sqrt{170}$