Question

find the distance between the two points in simplest radical form. (2,6) and (7, - 6)

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 $(x_1,y_1)=(2,6)$ and $(x_2,y_2)=(7, - 6)$. Then $x_2 - x_1=7 - 2=5$ and $y_2 - y_1=-6 - 6=-12$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=5^2 = 25$ and $(y_2 - y_1)^2=(-12)^2 = 144$. The sum is $25+144 = 169$.

Step4: Find the square - root

$d=\sqrt{169}=13$. But we want it in radical form before simplifying completely. So $d=\sqrt{5^{2}+(-12)^{2}}=\sqrt{25 + 144}=\sqrt{169}=13=\sqrt{13^{2}}$. In simplest radical form, $d = 13$.

Answer:

$13$