Question 53640
<pre><font size = 5><b>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 (x<sub>1</sub>, y<sub>1</sub>)
The coordinates of P are given as (x<sub>2</sub>, y<sub>2</sub>) = (-6, 6)

The midpoint formula is:

   m( (x<sub>1</sub> + x<sub>2</sub>)/2 , (y<sub>1</sub> + y<sub>2</sub>)/2 ) = m(-11, 13)

m( (x<sub>1</sub> + (-6))/2, (y<sub>1</sub> + 6)/2 ) = m(-11, 13)

          m( (x<sub>1</sub>-6)/2, (y<sub>1</sub>+6)/2 ) = m(-11,13)

So set the x-coordinates equal:

(x<sub>1</sub>-6)/2 = -11

Multiply both sides by 2

  (x<sub>1</sub>-6) = -22

  x<sub>1</sub> - 6 = -22

      x<sub>1</sub> = -16

Now set the y-coordinates equal:

(y<sub>1</sub>+6)/2 = 13

Multiply both sides by 2

  (y<sub>1</sub>+6) = 26

  y<sub>1</sub> + 6 = 26

      y<sub>1</sub> = 20

So the point is Q(-16, 20)

Edwin</pre>