Question

find the distance between the two points in simplest radical form.

Explanation:

Step1: Identify the coordinates

Let the first - point be $(-2,5)$ and the second - point be $(4,1)$.

Step2: Apply the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-2,y_1 = 5,x_2 = 4,y_2 = 1$. Then $x_2 - x_1=4-(-2)=6$ and $y_2 - y_1=1 - 5=-4$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=6^2 = 36$ and $(y_2 - y_1)^2=(-4)^2 = 16$. The sum is $36 + 16=52$.

Step4: Simplify the radical

$d=\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}$.

Answer:

$2\sqrt{13}$