Question

Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4)?
a 180degree rotation about the origin
a 90degree counterclockwise rotation about the origin and a translation down 4 units
a 90degree clockwise rotation about the origin and a reflection over the y-axis
a reflection over the y-axis and then a 90degree clockwise rotation about the origin

Answer 1

Correct answer: "a 90° clockwise rotation about the origin and a reflection over the y-axis."

Check (rotation then reflection):
- 90° clockwise: (x,y) -> (y, -x)
- reflect over y-axis: (x,y) -> (-x, y)
Combined: (x,y) -> (-y, -x)

Apply to the vertices:
- A(2,2) -> (-2,-2) = A'
- B(4,1) -> (-1,-4) = B'
- C(4,5) -> (-5,-4) = C'

The other options do not produce the given A', B', C' (e.g. 180° gives (-4,-1) and (-4,-5) for B and C).