Question

find the distance between the points (1, 1) and (0, 0). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Recall 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: Identify the points

Here, $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(1,1)$.

Step3: Substitute values

$d=\sqrt{(1 - 0)^2+(1 - 0)^2}=\sqrt{1^2+1^2}=\sqrt{1 + 1}$.

Step4: Simplify

$d=\sqrt{2}$.

Answer:

$\sqrt{2}$