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: Write the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Here, \(x_1 = 4,y_1 = 6,x_2 = 2,y_2 = 0\).

Step2: Substitute the values into the formula

Substitute the values: \(d=\sqrt{(2 - 4)^2+(0 - 6)^2}\).
First, calculate \((2 - 4)^2=(- 2)^2 = 4\) and \((0 - 6)^2=(-6)^2 = 36\).
Then \(d=\sqrt{4 + 36}\).

Step3: Simplify the expression

\(d=\sqrt{40}\).
Factor \(40\) as \(4\times10\), so \(d=\sqrt{4\times10}\).
Using \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}(a = 4,b = 10)\), we get \(d = 2\sqrt{10}\).

Answer:

\(2\sqrt{10}\)