Question

find the distance between the points (2, 4) and (3, 3). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify 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

Let $(x_1,y_1)=(2,4)$ and $(x_2,y_2)=(3,3)$. Then $d=\sqrt{(3 - 2)^2+(3 - 4)^2}$.

Step3: Calculate the values inside the square - root

First, $(3 - 2)^2=1^2 = 1$ and $(3 - 4)^2=(-1)^2 = 1$. So $d=\sqrt{1 + 1}$.

Step4: Simplify the radical

$d=\sqrt{2}$.

Answer:

$\sqrt{2}$