Question

Write a function to represent each series of transformations: • rotation of 90 degrees counterclockwise about the origin, point O, then a reflection across the x-axis • reflection across the y-axis, then a translation a units to the right and b units up • translation a units to the right and b units up, then a rotation of 180 degrees counterclockwise about the origin, then a reflection across the y-axis

Answer 1

For the first one, I believe you would need to use a rotation matrix; to rotate 90º counterclockwise, the matrices would look like $\left[\begin{array}{ccc}cos90&cos180\\sin90&sin180\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]$; you would then multiply those out. A reflection across the x-axis would be changing the sign of f(x) (from negative to positive or positive to negative), a reflection across the y-axis would be changing the sign of x, translation a units to the right would be subtracting a from x, translation b units up would be adding b to x. Rotation of 180º about the origin would be the same format as the first matrix, except it would be cos180 and cos0 on the top and sin180 sin0 on the bottom. Reflection across the y-axis would be changing the sign of x again.