Question

find the distance between the points (6, 10) and (8, 9). 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 $(x_1,y_1)=(6,10)$ and $(x_2,y_2)=(8,9)$. Then $x_1 = 6$, $y_1=10$, $x_2 = 8$, $y_2 = 9$.

Step3: Substitute the values into the formula

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

Step4: Calculate the squares

$d=\sqrt{4 + 1}$.

Step5: Simplify the expression

$d=\sqrt{5}$.

Answer:

$\sqrt{5}$