The line x - 6y + 11 = 0 bisects the join of (8, -1) and (0, k). Find the value of k.

The point (-3, 2) lies on the line ax + 3y + 6 = 0, calculate the value of a.

The point P divides the join of (2, 1) and (-3, 6) in the ratio 2 : 3. Does P lie on the line x - 5y + 15 = 0 ?

The line segment joining the points (5, -4) and (2, 2) is divided by the point Q in the ratio 1 : 2. Does the line x - 2y = 0 contain Q ?