Geometry translations

Question

Write a function to represent each series of transformations:

1. rotation of 90 degrees counterclockwise about the origin, point O, then a reflection across the x-axis
2. reflection across the y-axis, then a translation a units to the right and b units up
3. 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

a) (x, y) → (y, - x) → (y, x)

b) (x, y) → ( - x, y) → (- x - a, y + b)

c) (x, y) → (x - a, y + b) → (- x + a, - y - b) → (x - a, - y - b)

Answer 2

90 degrees CCW: (x,y) --> (-y,x)

reflection across x-axis: (-y,x) --> (-y,-x)

total: (x,y) --> (-y,-x)

reflection across y-axis: (x,y) --> (-x,y)

a units right and b units up: (-x,y) --> (-x + a, y+b)

total: (x,y) --> (-x + a,y + b)

a units right and b units up: (x,y) --> (x + a, y + b)

rotation of 180 CCW: (x+a, y+b) --> (-(x+a),-(y+b))

reflection about y axis: (-(x+a),-(y+b)) -->(x+a,-(y+b))

total: (x,y) --> (x+a,-(y+b))