Question

The vertices A(–2, –1), B(–3, 2), C(–1, 3), and D(0, 0) form a parallelogram. The vertices A’(–1, –2), B’(2, –3), C’(3, –1), and D’(0, 0) are the image of the parallelogram after a sequence of transformations. Which sequence of transformations could produce the image from the pre-image?
a reflection over the x-axis and then a reflection over the y-axis
a reflection over the y-axis and then a 90degree clockwise rotation about the origin
a 90degree clockwise rotation about the origin and then a reflection over the y-axis
a 90degree counterclockwise rotation about the origin and then a reflection over the x-axis

Answer 1

Answer: a reflection over the y-axis and then a 90° clockwise rotation about the origin.

Reason: Reflecting (x,y) over the y-axis gives (-x,y). A 90° clockwise rotation sends (u,v) to (v,-u). Composing gives (x,y) -> (-x,y) -> (y,x), i.e. the coordinates swap. Applying this to the vertices:

- A(−2,−1) -> (−1,−2) = A'
- B(−3,2) -> (2,−3) = B'
- C(−1,3) -> (3,−1) = C'
- D(0,0) -> (0,0) = D'

So option 2 is correct.