Find the point P(0,a) if it is midpoint A(2,5) and B(b. 3).

To find the mid point M of (x1,y1) and (x2,y2) we use the
formula.

Mx = (x1+x2)/2.

My =
(y1+y2)/2.

We have to find P(0, a)  which is the mid point
of A(0,5) and B(b,3).

We use the same formula to determine
P(0, a) or the y coordinate  Py = a  and the x coordinate Bx =
b.

Therefore Px = 0 = (Ax+By)/2 =
(0+b)/2.

0 = (0+b)/2

2*0 =
0+b. So b = 0.

Py =  a  = (Ay +By)/2 = (5+3)/2 = 8/4 
=4.

Therefore a =
4.

Therefore  a = 4 and b = 0 .