Route 3 crossfit gym is equidistant and collinear from fernando's healthshakes and nicole's cattery. fernando's healthshakes is located at point (-17, 17) and route 3 crossfit gym is located at point (-5.5, 3) on the coordinate plane. find the coordinates of nicole's cattery.

Refer to the diagram shown below.

Let (x,y) be the coordinates of Nicole's Cattery.

Because Crossfit Gym is equidistant and collinear from Fernando's HealthShakes, the coordinates of Crossfit Gym should be midway between Fernandos' and Nicole.
That is,
(x + (-17))/2 = -5.5
x = -11 + 17 = 6

Also,
(y + 17)/2 = 3
y = 6 - 17 = -11

Nicole's Cattery is at (6, -11)