The single transformation that maps triangle A onto triangle C is rotation of 180 degrees around the origin, as the composition of two reflections over both axes results in a full half-turn rotation.
The student's question involves mapping triangle A onto triangle C through a series of reflections. First, triangle A is reflected over the x-axis to form triangle B, then triangle B is further reflected over the y-axis to form triangle C.
Transformations in mathematics often deal with flipping, rotating, and sliding shapes on a coordinate plane, and reflections are a specific type of transformation.
A reflection over the x-axis changes the sign of the y-coordinate of each point within the shape, while a reflection over the y-axis changes the sign of the x-coordinate.
Since triangle A undergoes two reflections, first over the x-axis and then over the y-axis, the overall effect is that both the x and y coordinates switch their signs.
Therefore, the single transformation that maps triangle A onto triangle C is a rotation of 180 degrees around the origin.