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: 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: Substitute the values

Let $(x_1,y_1)=(7,4)$ and $(x_2,y_2)=(6,5)$. Then $x_2 - x_1=6 - 7=-1$ and $y_2 - y_1=5 - 4 = 1$.

Step3: Calculate the distance

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

Answer:

$\sqrt{2}$