Question

The point A(–3, 2) is reflected in the x-axis to the point A’. Point A’ is then reflected in the origin to point A”.

1. Write down the co-ordinates of A”.
2. Write down a single transformation that maps A onto A”.

Answer 1

i. The reflection in x-axis is given by M_x (x, y) = (x, –y).

A’ = reflection of A(–3, 2) in the x-axis = (–3, –2).

The reflection in origin is given by M_O (x, y) = (–x, –y).

A” = reflection of A’(–3, –2) in the origin = (3, 2)

ii. The reflection in y-axis is given by M_y (x, y) = (–x, y).

The reflection of A(–3, 2) in y-axis is (3, 2).

Thus, the required single transformation is the reflection of A in the y-axis to the point A”.