Question

find the distance between the points (1, 1) and (9, 7). 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 given points

Here, $x_1 = 1,y_1 = 1,x_2 = 9,y_2 = 7$. So $d=\sqrt{(9 - 1)^2+(7 - 1)^2}$.

Step3: Calculate the values inside the square - root

First, $(9 - 1)^2=8^2 = 64$ and $(7 - 1)^2=6^2 = 36$. Then $d=\sqrt{64 + 36}$.

Step4: Simplify the square - root

$64+36 = 100$, so $d=\sqrt{100}=10$.

Answer:

10