Question

find the distance between the points (-2, 0) and (1, -10). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Identify the distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Substitute the given points

Let $(x_1,y_1)=(-2,0)$ and $(x_2,y_2)=(1, - 10)$. Then $x_2 - x_1=1-(-2)=3$ and $y_2 - y_1=-10 - 0=-10$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=3^2 = 9$ and $(y_2 - y_1)^2=(-10)^2 = 100$. The sum is $9 + 100=109$.

Step4: Find the distance

$d=\sqrt{109}$.

Answer:

$\sqrt{109}$