Question

find the distance between the points (-1, -2) and (4, -9). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Identify 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 $(x_1,y_1)=(-1,-2)$ and $(x_2,y_2)=(4,-9)$. Then $x_2 - x_1=4-(-1)=5$ and $y_2 - y_1=-9 - (-2)=-7$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=(-7)^2 = 49$. The sum is $25 + 49=74$.

Step4: Find the distance

$d=\sqrt{74}$.

Answer:

$\sqrt{74}$