Question Bank | Unit 10A - Transformations

1. The triangle $A B C$ has vertices $A (2, 1)$ , $B (4, 1)$ and $C (4, 2)$ .

Draw, on the diagram below, the image of the triangle $A B C$ under

(a) an anticlockwise rotation of $90^{\circ}$ about the origin $O$ , labelling the image $X$ ,

(b) a reflection in the line $y = - x$ , labelling the image $Y$ .

2. Answer the whole of this question on a sheet of graph paper.

The triangle $A B C$ has vertices $A (2, 0)$ , $B (4, 4)$ and $C (0, 1)$ . The triangle $P Q R$ has vertices $P (8, - 2)$ , $Q (4, 0)$ and $R (7, - 4)$ . The triangle $L M N$ has vertices $L (- 2, - 7)$ , $M (- 6, - 9)$ and $N (- 3, - 5)$ . Draw these triangles on graph paper, using a scale of $1 cm to 1 unit$ on each axis, and label the vertices. $Δ A B C$ can be mapped onto $Δ P Q R$ by an anti-clockwise rotation about the origin followed by a translation.

(a) State the angle of rotation.

(b) Find the matrix which represents this rotation.

(c) Find the column vector of the translation.

(d) Given that $Δ A B C$ can be mapped onto $Δ P Q R$ by a single rotation, find the coordinates of the centre of this rotation.

(e) Given that $Δ A B C$ can be mapped onto $Δ L M N$ by a translation of $(\begin{matrix} 0 \\ - 3 \end{matrix})$ followed by a reflection in the mirror line $m$ , draw the line $m$ on your graph and label it clearly.

(f) Find the equation of $m$ .

3. (a) Describe completely a single transformation which maps $Δ A B C$ onto $Δ D E F$ .

(b) Describe completely a single transformation which maps $Δ A B C$ onto $Δ P Q R$ .

4. The whole of this question should be answered on graph paper.

(a) Using a scale of $1 cm to represent 1 unit$ on each axis, draw $x$ and $y$ axes, taking values of $x$ from $- 8 to 12$ and values of $y$ from $- 6 to 14$ . Draw and label the triangle $X$ , with vertices $(2, 4)$ , $(4, 4)$ and $(4, 1)$ .

(b) The single transformation $U$ maps the triangle $X$ onto the triangle $U (X)$ which has vertices $(6, 12)$ , $(12, 12)$ and $(12, 3)$ .

Draw and label the triangle $U (X)$ and describe fully the transformation $U$ .

(c) The transformation $R$ is a clockwise rotation of $90^{\circ}$ about the origin. Draw and label the triangle $R (X)$ .