Mathematics 4024 · O Level · Transformations

Transformations — practice question

(a)[1]

The shaded triangle, shown on the grid, is one part of a quadrilateral with a single line of symmetry. The area of the quadrilateral is twice the area of the triangle. Since the line of symmetry is not vertical, finish the quadrilateral.

(b)[2]

The shaded triangle, drawn on the grid, is one part of a shape whose area is $4$ times the shaded area and which has rotational symmetry of order $4$ about $M$. Complete the shape.

(c(i))[2]

Triangle $A$ is taken onto triangle $C$ by the translation $P$ with vector $\begin{pmatrix}3 \\ -1\end{pmatrix}$. Draw and label triangle $C$.

(c(ii))[1]

Triangle $A$ is taken onto triangle $B$ by a reflection $Q$. State the equation of the line of this reflection.

(c(iii))[2]

Triangle $C$ is taken onto triangle $D$ by reflection $Q$. Describe fully the single transformation that maps triangle $B$ onto triangle $D$.

(c(iv)(a))[1]

Transformation $R$ is a reflection in the line $y = 0$. $RQ(A) = E$. Find the coordinates of the vertices of triangle $E$.

(c(iv)(b))[2]

Describe fully the single transformation that maps triangle $A$ onto triangle $E$.

(c(iv)(c))[1]

Find the matrix that represents the transformation that maps triangle $A$ onto triangle $E$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate symmetrical shape

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