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

5×sqrt(2)

Step-by-step explanation:

point 1 = (3,9)

point 2 = (9,5)

to calculate the distance we use Pythagoras based on the coordination differences in x- and y-direction as the sides of a triangle (the direct distance being the Hypotenuse of that triangle).

distance² = (x-difference)² + (y-difference)²

as all arguments are squared, we don't need to worry, if we need to calculate the difference from point 1 to 2 or from point 2 to 1. also negative numbers turn into positive distances.

d² = (xd)² + (yd)² = (9-3)² + (5-9)² = 6² + (-4)² = 36+16 = 50

=>

d = sqrt(50) = sqrt(25×2) = 5×sqrt(2)