The diagram shows a triangle whose vertices are A(−2, 1), B(1, 7) and C(3, 1).

The diagram shows a triangle whose vertices are A(−2, 1), B(1, 7) and C(3, 1).
The point L is the foot of the perpendicular from A to BC, and M is the foot of
the perpendicular from B to AC.
(i) Find the gradient of the line BC.
(ii) Find the equation of the line AL.
(iii) Write down the equation of the line BM.

Solution: