Question

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

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-5-(-10)=- 5 + 10 = 5$, and $y_2 - y_1=-4 - 5=-9$.

Step3: Square the differences

Square the results from step 2. $(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=(-9)^2 = 81$.

Step4: Sum and find square - root

Sum the squared values and take the square - root. $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{25 + 81}=\sqrt{106}$.

Answer:

$\sqrt{106}$