Question

After a dilation with a center of (0, 0), a point was mapped as (1, 4) → (4, y). A student determined y to be 16. Evaluate the student's answer.

Answer 1

that looks correct, a dilation has the form

(x,y) -> (k*x , k*y)

Answer 2

so you know that k is 4, since
(1,4) -> (1*4, 4* ? )

Answer 3

a dilation with center (0,0)