The grid shows two trapeziums A and B. (a) Describe fully the transformation which maps A onto B.

(b) Draw the image of A after a stretch of invariant line x = −2 and stretch factor −3.

The diagram shows quadrilaterals A, B and C. (a) Describe fully a single transformation that maps:
(i) A onto C,

(ii) A onto B.

(b) Reflect B along the line x = 1.

(c) Find the coordinates of the image of point (10, 3) after the transformation by the matrix $\left(\begin{array}{cc}\frac{3}{5}& 0\\ \frac{2}{5}& -1\end{array}\right)$.

The diagram shows polygons D, G and H. (a) Describe fully the single transformation that maps:
(i) Polygon D onto polygon G,

(ii) Polygon D onto polygon H.

(b) On the grid, draw and label the image:
(i) R, of polygon G, after a reflection in the line x = 0,
(ii) M, of polygon D, after a stretch factor −1.5, with y = −2 invariant.

Triangles P, Q and R are shown on the diagram. (a) (i) Describe fully the single transformation H, that maps triangle P onto Q.

(ii) Describe fully the single transformation K, such that KH(P) = R.

(iii) (hx + k, y − k) is the image of (x, y) under the transformation KH.
Find the values of h and k.

(b) The matrix of transformation $\left(\begin{array}{cc}-1& 0\\ 2& -1\end{array}\right)$ maps triangle P onto U.
Draw and label triangle U.

The diagram shows triangles A, B and C. (a) (i) Plot and label the point T(5, 7) on the grid.
(ii) Rotate the point T through 90° clockwise about the origin. Label the image T'.
(b) Describe fully the single transformation that maps:
(i) Triangle B onto triangle A,

(ii) Triangle B onto triangle C.

(c) On the grid, draw the image of:
(i) Triangle B after a reflection in the line y = 2,
(ii) Triangle A after a stretch with scale factor 2 and invariant line the y-axis.

The diagram shows triangle ABC.

(a) A reflection in the line x = −1 maps triangle ABC onto triangle DEF.
Draw and label triangle DEF.

(b) A shear with factor 2 and invariant line y = 2 maps triangle ABC onto triangle GHI.
Draw and label triangle GHI.

(c) Describe fully the single transformation which maps triangle ABC onto triangle JKL.

(d) Triangle JKL is mapped onto triangle MNP. The vertices of triangle MNP are M(−3, −8), N(−3, −4) and P(−5, −4). Find a matrix which fully describes a single transformation which maps triangle JKL onto triangle MNP.

The diagram shows triangles A, B and C. (a) Describe fully the single transformation that maps triangle:
(i) A onto C,

(ii) A onto B.

(b) On the same grid, draw the image of triangle C after a shear, with invariant line y = 0 and shear factor 2.

The diagram shows triangles U, V, W, X. (a) Describe fully the single transformation that maps:
(i) Triangle V onto triangle X,

(ii) Triangle V onto triangle W,

(iii) Triangle V onto triangle U.

(b) On the same grid:
(i) Translate V using the vector $\left(\begin{array}{c}-3\\ 2\end{array}\right)$ and label the image V₁,

(ii) Rotate triangle V through 180° about the point (1, 3) and label the image V₂.

(c) Find the matrix which represents the transformation that maps V onto triangle X.

The diagram shows triangle A and triangle B. (a) Describe fully the single transformation which maps triangle A onto triangle B.

(b) Draw the enlargement of triangle A, centre (1, 1), scale factor −2 and label the triangle C.

(c) Reflect triangle A in the line y = x and label the image D.

(d) A transformation is represented by the matrix $\left(\begin{array}{cc}1& 1\\ 0& 1\end{array}\right)$.

(i) Draw the image of triangle A under this transformation. Label the image E.

(ii) Describe fully the single transformation which maps triangle A onto triangle E.