O-LevelMathematicsVectors and transformations4024/22 · Oct/Nov 2018 · Q79 Marks

Triangle A is drawn on the grid. [Figure 7.1] (a) Transformation P is represented by the matrix ( -2 0 0 -2 ). P maps triangle A onto triangle B.

(a)(i)Draw and label triangle B.[2]
(a)(ii)Describe fully the single transformation P.[2]
(a)(iii)Write down the ratio area of triangle A : area of triangle B.[1]
(b)Transformation Q is represented by the matrix ( 1 0 0 -1 ). Q maps triangle B onto triangle C. Draw and label triangle C.[2]
(c)Transformation Y is represented by the matrix ( 1 0 0 3 ). Y maps triangle A onto triangle D. Find the matrix that represents the transformation that maps triangle D onto triangle A.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[2] B1 for two correct vertices or two correct pairs of coordinates soi or correct size and orientation but wrong position
[2] B1 for enlargement
[1] 1 : 4 oe
[2] FT reflection of their triangle B in x-axis
[2] B1FT for two vertices correct
[2] B1 for (1 0 / 0 3)^-1 oe with k ≠ 1/3
[2] or for (1 0 / 0 1/3)

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