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1 markImage and Object Location (Transformations)

CSEC Mathematics · 2022 · Paper 2 · Question 10(a)(i)

The transformation matrix A = \begin{pmatrix}0 & -1\\1 & 0\end{pmatrix} represents a rotation of 90^\circ anticlockwise about the origin O. Matrix B = \begin{pmatrix}0 & -1\\-1 & 0\end{pmatrix} represents a reflection in the straight line y = -x.

Write the coordinates of P', the image of the point P(7, 11) after it undergoes a rotation by 90^\circ anticlockwise about the origin, O.

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  1. 10(a)(ii)T is the combined transformation of A followed by B. Determine the elements of the matrix representing the transformation T.[2 marks]
  2. 10(a)(iii)Describe, geometrically, the transformation represented by T.[2 marks]
  3. 10(b)Determine the value of k, given that the matrix C is singular.[2 marks]
  4. 10(c)(i)Express \vec{BX} in terms of u and v.[1 mark]
  5. 10(c)(ii)a)Express \vec{BM} in terms of u and v.[1 mark]
  6. 10(c)(ii)b)Using a vector method, show that the ratio YM : YA is 1 : 3. Show ALL working.[3 marks]

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