th1b prob5

Let the coordinates of this point be ( 4, y)

The point on the y axis closest to this point is (0, y)

So... we have this equation

Distance from (4, y) to (4, 1)   = Distance from (4, y) to (0, y)

( 4 - 4)^2 + (1 - y)^2  =  (4 - 0)^2 + ( y - y)^2          smplify

y^2 - 2y + 1   =  16

y^2 - 2y - 15  = 0      factor

(y - 5) ( y + 3) = 0

Since y  must be negative......y = -3

So.....the point is  ( 4, -3)