Transformations — reflection, rotation, enlargement, translation

When the question says "single transformation", naming a second one — or writing "enlargement and translation" — withholds the mark even if one part is right. Commit to ONE transformation and describe it fully; if a combination is asked for, give the single equivalent transformation instead.

Stating the scale factor but not the centre of enlargement earns only part of the marks — "describe fully" needs both. Always give the word enlargement, the scale factor (with its sign) AND the centre. Find the centre by ruling lines through pairs of corresponding vertices.

Reflecting in a diagonal line such as $y=x$ or $y=-x$ is done far less accurately than reflecting in a horizontal or vertical line. Check one vertex with the rule: $y=x$ sends $(x,y)\mapsto(y,x)$ and $y=-x$ sends $(x,y)\mapsto(-y,-x)$.

A negative scale factor puts the image on the OPPOSITE side of the centre and inverts it. Dropping the minus sign leaves the image on the same side (e.g. $-2$ giving $(2,6)$ instead of $(-2,-6)$). Multiply each vertex by $k$ with its sign, using $\text{image}=\text{centre}+k(\text{point}-\text{centre})$.

When a rotation has a centre other than the origin, rotating about $O$ instead gives the wrong image. Pin tracing paper at the STATED centre, or measure each vertex relative to that centre and turn that displacement by the angle in the stated direction (clockwise or anticlockwise).

A translation must be named as "translation" AND given as a column vector $\binom{x}{y}$. Writing "right 5, down 3" in words scores nothing, and reversing the vector to $\binom{-5}{3}$ loses the accuracy mark. Track one vertex to read off the vector: right is positive $x$, up is positive $y$.