Hello, I am stuck on a question in my FP1 textbook, in the practice exam section. I'm doing the OCR board.
It tells me that there are two 2 x 2 matrices R and S represent the following transformations in the x-y place.
R: a rotation through angle θ anticlockwise about origin
S: a stretch with scale factor 2 parallel to the x-axis (with the y-axis invariant)
RSR-¹ is denoted by M
I have found that M is:
The next part says the the point P has the column matrix:
And that the point Q is the image of P under the transformation represented by M.
I have found that the column matrix of Q would be:
But the next part asks me to show that the line joining P to Q makes an angle θ with the x-axis.
How would I show this last part? O____O Please help me and thank you very much in advance.