Respuesta :
The distance between the two points is [tex]2\sqrt{5}[/tex]
Explanation:
Given that the two points are [tex](-8,-2)[/tex] and [tex](-6,2)[/tex]
We need to determine the distance between the two points in simplest radical form.
The distance between the two points can be determined using the distance formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let us substitute the coordinates [tex](-8,-2)[/tex] and [tex](-6,2)[/tex] in the above formula, we get,
[tex]d=\sqrt{(-6+8)^2+(2+2)^2}[/tex]
Simplifying the terms, we get,
[tex]d=\sqrt{(2)^2+(4)^2}[/tex]
Squaring the terms, we get,
[tex]d=\sqrt{4+16}[/tex]
Adding, we get,
[tex]d=\sqrt{20}[/tex]
Simplifying, we have,
[tex]d=2\sqrt{5}[/tex]
Thus, the distance between the two points in simplest radical form is [tex]2\sqrt{5}[/tex]
