Question

find the distance between the two points in simplest radical form. (7,1) and (4,5)

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 $(x_1,y_1)=(7,1)$ and $(x_2,y_2)=(4,5)$. Then $x_2 - x_1=4 - 7=- 3$ and $y_2 - y_1=5 - 1 = 4$.

Step3: Substitute into formula

$d=\sqrt{(-3)^2+4^2}=\sqrt{9 + 16}$.

Step4: Simplify

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

Answer:

$5$