Question

question
find the distance between the two points in simplest radical form.
$(5,0)$ and $(2,4)$

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(5,0)\) and \((x_2,y_2)=(2,4)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(2 - 5)^2+(4 - 0)^2}\)

Step3: Simplify the expression inside the square root

\((2 - 5)^2=(-3)^2 = 9\) and \((4 - 0)^2=16\)
So \(d=\sqrt{9 + 16}\)

Step4: Calculate the sum

\(9+16 = 25\), then \(d=\sqrt{25}\)

Step5: Simplify the square root

\(\sqrt{25}=5\)

Answer:

\(5\)