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

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We are given that ( 3,-4) is the midpoint of AB and the coordinates of B are (1,6). We have to find the coordinates of A.

Let the coordinates of A be (x, y)

So as (3 , -4) is the mid point of A and B.

3 = (x + 1) / 2

=> 3*2 = x + 1

=> 6 = x + 1

=> x = 5

-4 = (y + 6) / 2

=> -4*2 = y + 6

=> y = -8 - 6

=> y = -14

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

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).