Question 133067
AB IS THE DIAMETER OF THE CIRCLE WHOSE CENTER IS O .IF THE COORDINATES OF O ARE (2,1) AND  THE  COORDINATES OF B (4,6). WHAT ARE THE  COORDINATES OF A . PLEASE SEND ME ANSWER  

O is the center of the circle.   The diameter is a segment with endpoints A and B.   This makes O the midpoint of segment AB.   The Midpoint formula is:

   M=(X1 +X2)/2,   (Y1 +Y2)/2

You are given the coordinates of the midpoint and one endpoint.   Adapt the formula:

    X coordinate of Midpoint=(X1 +X2)/2,   Y coordinate of Midpoint=(Y1 +Y2)/2
Substitute the numbers:

       2=(X+4)/2   ,    1=(Y+6)/2  Now solve each equation to find the X and Y coordinates of point A.

                 2=(X+4)/2   ,     1=(Y+6)/2 
cross multiply     4=X+4     ,    2=Y+6  cross multiply
                    X=0      ,   Y=-4
   A( 0,-4)