if m(-11,13) is the midpoint of segment PQ and 
the coordinates of P are (-6,6), find the 
coordinates of Q. 

Let the coordinates of the Q be (x1, y1)
The coordinates of P are given as (x2, y2) = (-6, 6)

The midpoint formula is:

   m( (x1 + x2)/2 , (y1 + y2)/2 ) = m(-11, 13)

m( (x1 + (-6))/2, (y1 + 6)/2 ) = m(-11, 13)

          m( (x1-6)/2, (y1+6)/2 ) = m(-11,13)

So set the x-coordinates equal:

(x1-6)/2 = -11

Multiply both sides by 2

  (x1-6) = -22

  x1 - 6 = -22

      x1 = -16

Now set the y-coordinates equal:

(y1+6)/2 = 13

Multiply both sides by 2

  (y1+6) = 26

  y1 + 6 = 26

      y1 = 20

So the point is Q(-16, 20)

Edwin