ECZ 2019 · O-Level Paper 2 · Question 7 — Geometrical Transformations
The vertices of triangle ABC are A(1, 1), B(1, 3) and C(3, 3). The vertices of triangle A1B1C1 are A1(-1, 1), B1(-3, 1) and C1(-3, 3).
(a) Using a scale of 1 cm to represent 1 unit on each axis, draw the x and y axes for -6 ≤ x ≤ 6 and -6 ≤ y ≤ 6. Draw and label triangles ABC and A1B1C1.[2]
Verified working — step 1
Draw the axes to the stated range.(b) Describe fully a single transformation that maps triangle ABC onto triangle A1B1C1.[2]
Verified working — step 1
Compare vertices: A(1, 1) → A1(-1, 1), B(1, 3) → B1(-3, 1), C(3, 3) → C1(-3, 3).(c) An enlargement maps triangle ABC onto triangle A2B2C2 with vertices A2(-2, -2), B2(-2, -6) and C2(-6, -6).
(c(i)) Draw and label triangle A2B2C2.[1]
Verified working — step 1
Plot the given image points A2(-2, -…(c(ii)) Find the scale factor.[1]
Verified working — step 1
Compare A(1, 1) → A2(-2, -2), B(1, 3) → B2(-2, -6), C(3, 3) → C2(-6, -6).(d) The transformation represented by the matrix 2001 maps triangle ABC onto triangle A3B3C3.
(d(i)) Find the coordinates of the vertices A3, B3 and C3.[2]
Verified working — step 1
2001 maps (x, y) to (2x, y).(d(ii)) Draw and label triangle A3B3C3.[1]
Verified working — step 1
Plot A3(2, 1), B3(2, 3), C3…(e) Triangle ABC is mapped onto triangle A4B4C4 with vertices A4(1, -2), B4(1, 0) and C4(3, -6).
(e(i)) Draw and label triangle A4B4C4.[1]
Verified working — step 1
Plot the given image points A4(1, …(e(ii)) Find the matrix representing this transformation.[2]
Verified working — step 1
Let the matrix be abcd: x' = ax + by, y' = cx + dy.The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.
Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.
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