Question

find the distance between the two points in simplest radical form. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Identify the coordinates

Let the two - points be $(x_1,y_1)$ and $(x_2,y_2)$. Assume the first point is $(-7,5)$ and the second point is $(-3, - 1)$.

Step2: Apply the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-7,y_1 = 5,x_2=-3,y_2=-1$. Then $x_2 - x_1=-3-(-7)=4$ and $y_2 - y_1=-1 - 5=-6$.

Step3: Calculate the distance

$d=\sqrt{(4)^2+(-6)^2}=\sqrt{16 + 36}=\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}$.

Answer:

$2\sqrt{13}$