Question

find the distance between the points (4,6) and (2,0).
write your answer as a whole number or a fully simplified radical expression. do not round.
units
save answer

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(4,6)\) and \((x_2,y_2)=(2,0)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(2 - 4)^2+(0 - 6)^2}\)

Step3: Simplify the expression inside the square - root

First, calculate \((2 - 4)^2=(-2)^2 = 4\) and \((0 - 6)^2=(-6)^2 = 36\)
Then \(d=\sqrt{4 + 36}=\sqrt{40}\)

Step4: Simplify the radical

Factor \(40\) as \(4\times10\), so \(\sqrt{40}=\sqrt{4\times10}=2\sqrt{10}\)

Answer:

\(2\sqrt{10}\)