Question

find the distance between the two points. (-1,-2) (3,-1) enter the number that goes beneath the radical symbol.

Explanation:

Step1: Identify distance - formula components

Let $(x_1,y_1)=(-1,-2)$ and $(x_2,y_2)=(3,-1)$. The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. We need to find $(x_2 - x_1)^2+(y_2 - y_1)^2$.

Step2: Calculate $(x_2 - x_1)^2$

$x_2 - x_1=3-(-1)=4$, so $(x_2 - x_1)^2 = 4^2=16$.

Step3: Calculate $(y_2 - y_1)^2$

$y_2 - y_1=-1-(-2)=1$, so $(y_2 - y_1)^2 = 1^2 = 1$.

Step4: Find the sum

$(x_2 - x_1)^2+(y_2 - y_1)^2=16 + 1=17$.

Answer:

17