Transformations and Vectors

Describing a transformation completely enough to earn the marks, and the column-vector arithmetic that turns geometry into calculation.

หลักสูตรแกนกลาง / สสวท.: การวัดและเรขาคณิต (Geometry and Measure)ครอบคลุม ม.2 บทที่ 4 การแปลงทางเรขาคณิต · ม.5 เวกเตอร์
Common Core (US): 8.G, N-VM
Cambridge: IGCSE 0580 — Topic 7: Transformations and vectors (Core and Extended)

10.1 Describing a transformation

Transformation	Name it, and give…
reflection	the equation of the mirror line
rotation	the centre, the angle AND the direction
translation	a column vector
enlargement	the centre and the scale factor

What a complete description must state

ข้อควรระวัง

The marks are for the DESCRIPTION, not the drawing. "Rotation of $9 0^{\circ}$ " is incomplete; "rotation of $9 0^{\circ}$ clockwise about $(0, 0)$ " is the answer. Naming two transformations when one is asked for loses the mark outright.

Transformation	$(x, y)$ becomes
reflection in the $x$ -axis	$(x, - y)$
reflection in the $y$ -axis	$(- x, y)$
reflection in $y = x$	$(y, x)$
rotation $9 0^{\circ}$ anticlockwise about $O$	$(- y, x)$
rotation $18 0^{\circ}$ about $O$	$(- x, - y)$
enlargement, centre $O$ , factor $k$	$(k x, k y)$

Coordinate rules

เคล็ดลับ

A negative scale factor puts the image on the opposite side of the centre and turns it upside down. It is still called an enlargement even when the image is smaller or inverted — the word is technical here, not descriptive.

📖 2 more sections of this chapter are being checked

The whole chapter is written; we read it back section by section before releasing it, because maths nobody has checked should not be on a public page. What is open is complete — nothing here is abridged.

Read it — now practise it

Generate a worksheet on this topic, or sit a timed mock paper.

Build a worksheet Practice arena