Question

find the distance between the points (9, 2) and (3, 10). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Substitute the values

Let $(x_1,y_1)=(9,2)$ and $(x_2,y_2)=(3,10)$. Then $d=\sqrt{(3 - 9)^2+(10 - 2)^2}$.

Step3: Calculate the differences

$3-9=-6$ and $10 - 2 = 8$. So $d=\sqrt{(-6)^2+8^2}$.

Step4: Calculate the squares

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

Step5: Add the values inside the square - root

$36+64 = 100$. So $d=\sqrt{100}$.

Step6: Simplify the square - root

$\sqrt{100}=10$.

Answer:

10