Question

find the distance between the points (8, 10) and (9, 4). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Here, $(x_1,y_1)=(8,10)$ and $(x_2,y_2)=(9,4)$.

Step2: Substitute the values into the formula

$d=\sqrt{(9 - 8)^2+(4 - 10)^2}=\sqrt{1^2+(-6)^2}$.

Step3: Calculate the squares

$d=\sqrt{1 + 36}$.

Step4: Simplify the expression

$d=\sqrt{37}$

Answer:

$\sqrt{37}$ units