The distance between the two points is ![2\sqrt{5}](/tpl/images/0548/7342/0bea1.png)
Explanation:
Given that the two points are
and ![(-6,2)](/tpl/images/0548/7342/da204.png)
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,
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](/tpl/images/0548/7342/c9678.png)
Let us substitute the coordinates
and
in the above formula, we get,
![d=\sqrt{(-6+8)^2+(2+2)^2}](/tpl/images/0548/7342/d031f.png)
Simplifying the terms, we get,
![d=\sqrt{(2)^2+(4)^2}](/tpl/images/0548/7342/5f420.png)
Squaring the terms, we get,
![d=\sqrt{4+16}](/tpl/images/0548/7342/5718a.png)
Adding, we get,
![d=\sqrt{20}](/tpl/images/0548/7342/01e99.png)
Simplifying, we have,
![d=2\sqrt{5}](/tpl/images/0548/7342/9a52f.png)
Thus, the distance between the two points in simplest radical form is ![2\sqrt{5}](/tpl/images/0548/7342/0bea1.png)