Question

find the distance between the points (10, 6) and (7, 10). write your answer as a whole number or a fully simplified radical expression. do not round.

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: Assign values

Let $(x_1,y_1)=(10,6)$ and $(x_2,y_2)=(7,10)$. Then $x_2 - x_1=7 - 10=- 3$ and $y_2 - y_1=10 - 6 = 4$.

Step3: Calculate squares

$(x_2 - x_1)^2=(-3)^2 = 9$ and $(y_2 - y_1)^2=4^2 = 16$.

Step4: Sum squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=9 + 16=25$.

Step5: Find square - root

$d=\sqrt{25}=5$.

Answer:

5