Question

question
find the distance between the two points in simplest radical form.
$(3,0)$ and $(-3,-8)$

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(3,0)\) and \((x_2,y_2)=(-3,-8)\)

Step2: Apply the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(-3 - 3)^2+(-8 - 0)^2}\)

Step3: Simplify the expression inside the square root

\((-3 - 3)^2=(-6)^2 = 36\) and \((-8 - 0)^2=(-8)^2=64\)
So \(d=\sqrt{36 + 64}\)

Step4: Add the numbers inside the square root

\(36+64 = 100\), then \(d=\sqrt{100}\)

Step5: Simplify the square root

\(\sqrt{100}=10\)

Answer:

\(10\)