Question

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

Explanation:

Step1: Identify the 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: Assume the points

Let's assume the two - points from the graph are $(x_1,y_1)$ and $(x_2,y_2)$. Suppose the first point has coordinates $(x_1,y_1)=(-1,7)$ and the second point has coordinates $(x_2,y_2)=(7, - 5)$.

Step3: Calculate differences

Calculate $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=7-(-1)=8$.
$y_2 - y_1=-5 - 7=-12$.

Step4: Substitute into formula

Substitute into the distance formula:
$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{8^2+(-12)^2}=\sqrt{64 + 144}=\sqrt{208}$.

Step5: Simplify the radical

Factor 208: $208 = 16\times13$.
So, $\sqrt{208}=\sqrt{16\times13}=4\sqrt{13}$.

Answer:

$4\sqrt{13}$