Question

find the distance between the points (7, 4) and (6, 5). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 7,y_1 = 4,x_2 = 6,y_2 = 5$.

Step2: Substitute values

$d=\sqrt{(6 - 7)^2+(5 - 4)^2}=\sqrt{(- 1)^2+1^2}$.

Step3: Calculate squares

$(-1)^2=1$ and $1^2 = 1$, so $d=\sqrt{1 + 1}$.

Step4: Simplify

$d=\sqrt{2}$.

Answer:

$\sqrt{2}$