Question

find the distance between the two points. (-5,5) (2,-2) enter the number that goes beneath the radical symbol.

Explanation:

Step1: Identify distance formula

The distance $d$ 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, $(x_1,y_1)=(-5,5)$ and $(x_2,y_2)=(2,-2)$.

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

$x_2 - x_1=2-(-5)=7$, so $(x_2 - x_1)^2 = 7^2=49$.

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

$y_2 - y_1=-2 - 5=-7$, so $(y_2 - y_1)^2=(-7)^2 = 49$.

Step4: Find sum

$(x_2 - x_1)^2+(y_2 - y_1)^2=49 + 49=98$.

Answer:

98