Question

The point A(4, 6) is first reflected in the origin to point A’. Point A’ is then reflected in the y-axis to the 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 origin is given by M_O (x, y) = (–x, –y).

A’ = reflection of A(4, 6) in the origin = (–4, –6)

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

A” = reflection of A’(–4, –6) in the y-axis = (4, –6)

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

The reflection of A(4, 6) in x-axis is (4, –6).

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