ECZ 2017 · GCE Paper 2 · Question 7 — Geometrical Transformations
Answer on graph paper (1cm to 1 unit, -6 ≤ x ≤ 10, -6 ≤ y ≤ 12). Quadrilateral ABCD has vertices A(1,2), B(2,1), C(3,2), D(2,3). A1B1C1D1 has vertices A1(3,2), B1(6,1), C1(9,2), D1(6,3). A3B3C3D3 has vertices A3(-2,-4), B3(-4,-2), C3(-6,-4), D3(-4,-6).
(a(i)) Draw and label quadrilaterals ABCD and A1B1C1D1.[2]
Verified working — step 1
Plot A(1,2), B(2,1), C(3,2), D(2,3) and join AB, BC, CD, DA to form quadrilateral ABCD (a small squarerhombusshape). Then plot A1(3,2), B1(6,1), C1(9,2), D1…(a(ii)) Describe fully a single transformation which maps quadrilateral ABCD onto quadrilateral A1B1C1D1.[3]
Verified working — step 1
Compare corresponding coordinates:(b(i)) The 1031 maps ABCD onto A2B2C2D2. Find the coordinates of quadrilateral A2B2C2D2.[3]
Verified working — step 1
Apply the 1031 to each point (x,y) using (x', y') = (1x+0y, 3x+1y):(b(ii)) Draw and label quadrilateral A2B2C2D2.[1]
Verified working — step 1
Plot A2(1,5), B2(2,7), C2(3,11), D2(2,9) on the same grid and join A2B2, B2C2, C2D2, D2A2 to form q…(c) Describe fully the transformation which maps quadrilateral ABCD onto quadrilateral A3B3C3D3.[3]
Verified working — step 1
Compare each point of ABCD to A3B3C3D3: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.
Have a different question?
Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.
Search any past-paper question