1. Draw a triangle with vertices A = (2, 1), B = (1, 4), C = (5, 2)

(a) Reflect the triangle in the x-axis and label the result A´ B´ C´

(b) Rotate A´ B´ C´ through an angle of 180°, centre (0, 0) and label the result A´´  B´´ C´´.

(c) What single transformation maps ABC to A´´  B´´ C´´?

2. The triangle shown below is first reflected in the y-axis (transformation M). It is then enlarged, centre (0, 0) the origin, with scale factor − 0.5 (transformation E).

M maps ABC to A´B´C´  and E then maps A´B´C´ to A´´  B´´ C´´ .

(a) Draw triangles A´B´C´ and A´´  B´´ C´´.

(b) Name a set of points that is invariant under M.

(c) Which point is invariant under E?

(d) Which point or line is invariant under EM (that is, M followed by E)?

(e) If N is the transformation "reflect in the x- axis" which of the following is not equivalent to the combined transformation EM?

(i) EN

(ii) ME

(iii) NMNE