Transformations and Congruence

Moving a shape without changing it — reflection, rotation and translation — and enlargement, which changes exactly one thing.

หลักสูตรแกนกลาง / สสวท.: การวัดและเรขาคณิต (Geometry and Measure)ตรงกับ ม.2 บทที่ 4 การแปลงทางเรขาคณิต และบทที่ 8 ความเท่ากันทุกประการ
Common Core (US): 8.G, G-CO
Cambridge: Lower Secondary Stage 8 — Geometry and Measure: position and transformation

10.1 Reflection, rotation and translation

Transformation	You must state	What changes
reflection	the mirror line	the shape is flipped over
rotation	centre, angle and direction	the shape turns
translation	how far across and up	position only

What each one needs to be described completely

ข้อควรระวัง

A rotation described without its centre is incomplete, and the marks go with the description rather than the drawing. "Rotation of $9 0^{\circ}$ " is not an answer; "rotation of $9 0^{\circ}$ clockwise about $(0, 0)$ " is.

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 the origin	$(- y, x)$
rotation $18 0^{\circ}$ about the origin	$(- x, - y)$
translation $a$ across, $b$ up	$(x + a, y + b)$

The coordinate rules

เคล็ดลับ

Reflecting in the $x$ -axis changes the sign of $y$ — the opposite of what most people guess. Sketch roughly and ask which quadrant the point should land in before writing anything down.

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