Question

what is the distance in the standard (x,y) coordinate plane between the points (2,0) and (0,4)? 2√5 √13 4 6

Explanation:

Step1: Recall the distance formula

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

Step2: Substitute the given points

Here, \(x_1 = 2,y_1 = 0,x_2 = 0,y_2 = 4\). Then \(d=\sqrt{(0 - 2)^2+(4 - 0)^2}\).

Step3: Calculate the values inside the square - root

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

Step4: Simplify the expression

\(d=\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\).

Answer:

\(2\sqrt{5}\) (the first option)