Question

find the distance between the points (1, 10) and (9, 4). 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 $(x_1,y_1)=(1,10)$ and $(x_2,y_2)=(9,4)$. Then $x_2 - x_1=9 - 1 = 8$ and $y_2 - y_1=4 - 10=-6$.

Step3: Calculate the squares

$(x_2 - x_1)^2=8^2 = 64$ and $(y_2 - y_1)^2=(-6)^2 = 36$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=64 + 36=100$.

Step5: Find the square - root

$d=\sqrt{100}=10$.

Answer:

$10$