Hi Sonia! Here is the next part to show that P, Q and M are collinear.

The technique is seen in the vectors topic in E Maths, which you have recently learnt or will be learning in vectors in E Maths.

To find the coordinates of M, we need to solve the two equations simultaneously to find the two coordinates before obtaining the midpoint M which is simply the average x-values and y-values of the two points of intersection R and S.

To show that P, Q and M are collinear, we need to prove two things:

1. PQ and QM (using PM is also possible, any two will do) must have the same gradient. This is analogous to PQ and QM having the same direction vector (in the vectors topic). In fact, the direction vector does tell you the gradient of a vector (the bottom number divided by the top number).

2. There must be a common coordinate between the two lines. Otherwise, we can only prove that the two lines are parallel.

Hopefully you understand my workings! Let me know if you do not understand my workings or my workings are too messy or you need more help in this topic.