Successive transformations and order

Apply a sequence of transformations one step at a time. The intermediate image becomes the input to the next step. Keep a small coordinate table so the order stays visible.

Example

For \(P(1,2)\), first translate by \(\begin{pmatrix}3\\0\end{pmatrix}\), obtaining \((4,2)\), then reflect in the y-axis, obtaining \((-4,2)\). Reversing the order gives \((-1,2)\) then \((2,2)\), a different result.

To undo a sequence, reverse its order and undo each transformation: reverse a translation vector, reverse a rotation, reflect again in the same line, or use reciprocal scale factor about the same enlargement centre. Describe each step fully.