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:

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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