The line segment joining the points A(3, 2) and B(5, 1) is divided at the points P in the ratio 1 : 2 and it lies on the line 3x - 18y + k = 0. Find the value of k.

The mid-point of the line segment joining the points (3m, 6) and (-4, 3n) is (1, 2m - 1). Find the values of m and n.

The coordinates of the mid-point of the line segment PQ are (1, -2). The coordinates of P are (-3, 2). Find the coordinates of Q.

Find the coordinates of the point which is three-fourth of the way from A(3, 1) to B(-2, 5).