Transformations
Reflection and rotation
- A transformation changes a shape's position or size. To describe one, give all its details.
- Reflection flips over a mirror line (give the line's equation). Reflect $(3,2)$ in the $y$-axis → $(-3,2)$ (only $x$'s sign changes).
- Rotation turns about a centre (give centre, angle, direction). Rotate $(3,1)$ by $90^{\circ}$ anticlockwise about $O$: rule $(x,y)\to(-y,x)$ → $(-1,3)$.
Practice
Reflect the point (3, 2) in the y-axis. The image is (a, 2). What is a?
Reflecting in the y-axis flips the sign of x: a = −3.
Enlargement and translation
- Enlargement changes size by a scale factor $k$ from a centre (give centre and $k$). Enlarge $(1,2)$ from $O$ by $k=2$ → $(2,4)$.
- (Extended) $k$ may be fractional (smaller) or negative (other side of the centre).
- Translation slides with no turning, by a column vector $\begin{pmatrix} x \\ y \end{pmatrix}$. Translate $(5,3)$ by $\begin{pmatrix} -2 \\ 4 \end{pmatrix}$ → $(3,7)$.
Practice
Translate (5, 3) by the vector (−2, 4). The image is (3, b). What is b?
Move 4 up: 3 + 4 = 7.
Practice
Which transformation changes the size of a shape?
Only enlargement changes size; the other three keep it congruent.
You've got it
Key idea
- reflection (mirror line), rotation (centre, angle, direction)
- enlargement (centre, scale factor $k$), translation (column vector)
- describe each fully — that's what earns the marks