Question

A, P and, B are collinear and P lies midway between A and C. A lies at (4+2/5a, -a) P lies at (a +5,-2a-1)and B lies at(28/5a ,3/5a)​

Answer 1

Step-by-step explanation:

If three points P(x1,y1),Q,R(x2,y2) are collinear.

⇒PQ=QR and Q is the midpoint of PR

The mid point Q=(2x1+x2,2y1+y2)

Given, the points A(5,2),B(3,4) and C(x,y) are collinear and AB=BC 

⇒ B is the mid-point of AC.

Using midpoint formula, 

     (2x+5,2y+2)=(3,4)

⟹2x+5=3 and 2y+2=4

⟹x+5=6 and y+2=8

⟹x=1 and y=6

Hence, the coordinates of C are (1,6).