Hello,

Can you please assist with this:

What are the (x, y) coordinates of point Q if point Q is equidistant from the four
vertices of square ABCD and the (x, y) coordinates of A, B, and D are,
respectively, (2, 1), (2, 4), and (5, 1)?

(A) (2.5, 2)
(B) (2.5, 2.5)
(C) (3.5, 2.5)
(D) (4, 4)
(E) (5, 4)

OA: C

My approach was as follows:

I was thinking that since AC is a diagonal, length of AC = (s)(square root of 2) = 3.sqroot of 2
Hence, AQ = 1.5 x sqroot of 2

Can you please tell me why this would be in-correct?

Thanks,
Sri