Question

find the distance between the points (0, 5) and (4, 6). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify 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: Assign values

Here $x_1 = 0,y_1 = 5,x_2 = 4,y_2 = 6$. Substitute into the formula: $d=\sqrt{(4 - 0)^2+(6 - 5)^2}$.

Step3: Calculate expressions inside square - root

First, $(4 - 0)^2=4^2 = 16$ and $(6 - 5)^2=1^2 = 1$. Then $d=\sqrt{16 + 1}$.

Step4: Simplify

$d=\sqrt{17}$.

Answer:

$\sqrt{17}$