Find the point A if the point ( 3,-4) is midpoint of AB and B is (1,6).

The mid point of AB is (3,-4) and B
(1,6).

Therefore we use mid point formula M(x,y) = ((Ax+Bx)/2,
Ay+By)/2)

Therefore (3, -4) = (( Ax  +1)/2 , (Ay
+6)/2)

We  equate x coordinates and y coordinates separately and
solve for Ax and Ay:

3 = (Ax+1)/2.

6 =
Ax+1. So Ax = 6-1 = 5.

-4 = (Ay +
6)/2.

-8 = Ay +6.  So Ay = -8 -6 =
-14.

Therefore the  coordinates of A  = ( 5,
-14).