Step-by-step explanation:
3
Let D be the mid point of side BC, [B(2, - 1), C(5, 2)].
Therefore, by mid-point formula:

4 (a) 
Equation of line AB[A(2, 1), B(-2, - 11)] in two point form is given as:
 
 
is the equation of line AB. 
Now we have to check whether C(4, 7) lie on line AB or not. 
Let us substitute x = 4 & y = 7 on the Left hand side of equation of line AB and if it gives us 0, then C lies on the line. 
 
 
Hence, point C (4, 7) lie on the straight line AB.
4(b)
Like we did in 4(a), first find the equation of line AB and then substitute the coordinates of point C in equation and if they satisfy the equation, then all the three points lie on the straight line.