Question

find the distance between the points (1, -7) and (-2, 0). 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 $(x_1,y_1)=(1,-7)$ and $(x_2,y_2)=(-2,0)$. Then $x_2 - x_1=-2 - 1=-3$ and $y_2 - y_1=0-(-7)=7$.

Step3: Calculate the square - terms

$(x_2 - x_1)^2=(-3)^2 = 9$ and $(y_2 - y_1)^2=7^2 = 49$.

Step4: Sum the square - terms and find the square root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{9 + 49}=\sqrt{58}$.

Answer:

$\sqrt{58}$