Question

find the distance between the two points in simplest radical form.

Explanation:

Since the points are not labeled, assume the two points are $(x_1,y_1)$ and $(x_2,y_2)$. The distance formula between two points in a coordinate - plane is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

However, without the actual coordinates of the two points, we cannot calculate the distance. If we assume the points are $(- 6,-4)$ and $(-2,-6)$ (for example, if these were the correct coordinates from visual inspection):

Step1: Identify the coordinates

Let $(x_1,y_1)=(-6,-4)$ and $(x_2,y_2)=(-2,-6)$.

Step2: Calculate differences

$x_2 - x_1=-2-(-6)=-2 + 6 = 4$ and $y_2 - y_1=-6-(-4)=-6 + 4=-2$.

Step3: Apply distance formula

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{4^2+(-2)^2}=\sqrt{16 + 4}=\sqrt{20}$.

Step4: Simplify the radical

$\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}$.

If we had the actual correct coordinates from the graph, we would follow these steps with the correct values. But if we assume the above - mentioned example coordinates:

Answer:

$2\sqrt{5}$