Question

find the distance between the points (9, 1) and (0, 9). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 9,y_1 = 1,x_2=0,y_2 = 9$.

Step2: Substitute values

$d=\sqrt{(0 - 9)^2+(9 - 1)^2}=\sqrt{(-9)^2+8^2}$.

Step3: Calculate squares

$(-9)^2=81$ and $8^2 = 64$, so $d=\sqrt{81 + 64}$.

Step4: Add values inside square - root

$81+64 = 145$, so $d=\sqrt{145}$.

Answer:

$\sqrt{145}$