Question

find the distance between the points (9, 10) and (0, 7). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign the values of the points

Let $(x_1,y_1)=(9,10)$ and $(x_2,y_2)=(0,7)$. Then $x_2 - x_1=0 - 9=-9$ and $y_2 - y_1=7 - 10=-3$.

Step3: Substitute into the formula

$d=\sqrt{(-9)^2+(-3)^2}=\sqrt{81 + 9}=\sqrt{90}$.

Step4: Simplify the radical

$\sqrt{90}=\sqrt{9\times10}=3\sqrt{10}$.

Answer:

$3\sqrt{10}$