Question

If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?

Answer 1

A is the point (-4, 1)

i) reflection over the y-axis projects a point (a, b) to (-a, b):

(-4, 1) is projected to (4, 1), 

ii) reflection over the x axis projects a point (a, b) to (a, -b):

(4, 1) is projected to (4, -1),

iii) rotation 180 degrees: projects (a, b) to (-a, -b):

so (4, -1) is projected to (-4, 1)


Answer: A'(-4, 1)