Exam-Style Questions on Transformations

Shape A can be transformed to shape B by a reflection in the y-axis followed by a translation \( {c \choose d} \)

Find the value of \(c\) and the value of \(d\).

Worked Solution

The shape A is drawn on the coordinate grid as shown below.

Sally and Eddie each transform the shape A onto shape B.

• Sally uses a reflection in the line y = 7 followed by a rotation of 90^o anticlockwise about the point (9,9).
• Eddie transforms shape A first with a reflection in the line \(y = x\) followed by his favourite transformation.

(a) Draw and label shape B.

(b) Describe fully Eddie's favourite transformation.

Worked Solution

The diagram shows a red trapezium drawn on a grid.

The trapezium is subjected to two transformations, one after the other.

One transformation is a reflection in the line \(y=x\).

The other transformation is a reflection y-axis.

Does it matter in which order these transformations are made? Explain your answer.

Worked Solution

(a) Shape \(A\) is translated to shape \(B\) using the vector \( \begin{pmatrix}m\\n\\ \end{pmatrix}\). What are the values of \(m\) and \(n\)?

(b) Vectors \(a, b, c, d\) and \(e\) are drawn on an isometric grid. Write each of the vectors \(c, d\) and \(e\) in terms of \(a\) and/or \(b\).

Worked Solution

The diagram shows a trapezium A on a grid.

Trapezium A is reflected in the line \(x=10\) to give trapezium B.

Trapezium B is translated by \(\begin{pmatrix} -6 \\ -3 \\ \end{pmatrix} \) to give trapezium C.

(a) Draw the trapezia B and C on the grid above.

(b) Trapezium C is reflected in the line \(y=5\) to give trapezium D. What are the coordinates of the centre of a 180° rotation that would map trapezium D onto trapezium A?

Worked Solution

The following points have been plotted then joined up in order to make an irregular hexagon.

Enlarge the hexagon by a scale factor of \(2\frac12 \), centre (-3,-4).

Worked Solution

Describe fully the single transformation that maps trapezium A onto trapezium B.

Worked Solution

The graph of the curve with equation y = \(f(x)\) is shown on the grid below.

(a) On the grid above, sketch the graph of the curve with equation \(y = f(–x)\)

The red curve with equation \(y = x^2-5x+4\) is transformed by a translation to give the blue curve such that the point (2.5, -2.25) on the red curve is mapped to the point (-2.5, -2.25) on the blue curve.

(b) Find an equation for the blue curve.

Worked Solution

Part of the graph of a function, \(f\) , is shown in the following diagram. The graph of \(y = f(x)\) has a y-intercept at \((0, 1.5)\) , an x-intercept at \((a , 0)\) and horizontal asymptotes \(y = 5\) and \(y = -2\).

Consider the function \(g(x) = |f(|x|)| \)

(a) Sketch the graph of \(y = g(x)\), labelling any axis intercepts and giving the equation of the asymptotes.

(b) Find the possible values of \(k\) such that \( (g(x))^2 = k \) has exactly four solutions.

Worked Solution