Theory question 114
Vectors and Transformations(Questions 14 and 15 are for candidates in Ghana, Sierra Leone and The Gambia only.)
(a) Using a scale of 2 cm to 2 units on both axes, draw, on a graph paper, two perpendicular axes Ox and Oy for −8 ≤ x ≤ 8 and −8 ≤ y ≤ 8.
(b) Draw the ΔPQR with vertices P(2, 5), Q(2, −1) and R(8, 4).
(c) Describe fully, two different transformations that map P to Q.
(d) Draw the image ΔP1Q1R1 of ΔPQR under a rotation through 90° anticlockwise about O.
(e) Find the vector PP1.
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(a), (b) Axes drawn to scale; triangle with P(2, 5), Q(2, −1), R(8, 4).
(c) Any two of: a reflection in the line y = 2; a translation by the vector (0, −6); a rotation of 180° about (2, 2).
(d) Rotation 90° anticlockwise about O maps (x, y) to (−y, x): P1(−5, 2), Q1(1, 2), R1(−4, 8).
(e) PP1 = (−5 − 2, 2 − 5) = (−7, −3), written as a column vector.
P and Q have the same x-coordinate, so the mirror line is halfway between y = 5 and y = −1.