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?