Congruency, Enlargement and Combined Transformations · Form 5
Congruency, Enlargement and Combined Transformations: Key Terms
The key Congruency, Enlargement and Combined Transformations terms you need for SPM Mathematics, defined plainly in English, Malay and Chinese.
- Congruency Two shapes are congruent when they have exactly the same shape and size.
- Scale factor The number k by which an enlargement multiplies lengths; areas multiply by k².
- Enlargement A transformation that changes a shape’s size by a scale factor while keeping its shape.
- Rotation A transformation that turns a shape about a fixed centre by an angle and direction.
- Reflection A transformation that flips a shape across a line to give a mirror image.
- Translation A transformation that slides every point of a shape the same distance and direction.
- Object and image The original shape (object) and its result after a transformation (image).
- Centre of enlargement The fixed point from which an enlargement is measured.
- Congruent Having exactly the same shape and size.
Term pairs students mix up
- Congruent vs similar, congruent shapes are identical in shape and size (one fits exactly on the other); similar shapes share the shape but differ in size, linked by a scale factor. Every congruent pair is similar with k = 1, but not the reverse.
- Object vs image, the object is the original shape before the transformation; the image is the result after it. Exam labels use a prime: P is the object, P' (P-prime) is the image.
- Scale factor vs area factor, the scale factor k compares lengths; the area factor is k², comparing areas. A scale factor of 3 gives an area factor of 9.
- Centre of enlargement vs centre of rotation, both are fixed points, but the centre of enlargement lies on the rays through matching points and controls size, while the centre of rotation is the pivot the shape turns about.
- Reflection vs rotation, a reflection flips the shape over a mirror line, producing a mirror image; a rotation turns it about a point through an angle without flipping it.
- Translation vs enlargement, a translation slides the shape with no change in size or orientation; an enlargement changes the size by a scale factor about a centre.
How these terms show up in real SPM questions
- 'Describe fully the transformation' is the trigger for the whole checklist: name the type, then give its centre or mirror line, its angle or scale factor, and its direction.
- '…maps triangle P onto triangle Q', or 'the image of P', tells you which shape is the object and which is the image, the object is named first, the image second.
- 'A single transformation' is a signal that two moves have been combined, and you must find the one equivalent transformation rather than list the two.
- 'With centre C and scale factor k' is the standard wording for an enlargement; a negative or fractional k is deliberate, so read it carefully.
- 'Invariant', or 'the point that does not move', points to a fixed point, the centre of an enlargement or rotation, or any point on a mirror line.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
In exam wording, how do I tell the object from the image?
The object is the starting shape, named first in the sentence; the image is what it becomes after the transformation, named second and often written with a prime, like P'. A phrase such as 'P is mapped onto P'' means P is the object and P' the image.
You always transform from object to image, never the reverse.
A question mentions an 'invariant point' what does that mean here?
An invariant point is one that does not move under the transformation. In an enlargement it is the centre; in a rotation it is the centre of rotation; in a reflection every point on the mirror line is invariant.
Spotting it often helps you locate a centre or a mirror line quickly.
Can two shapes ever be both similar and congruent?
Yes. Congruent shapes are a special case of similar shapes where the scale factor is exactly 1, same shape and same size.
So every congruent pair is also similar, but similar shapes are only congruent when their scale factor is 1. If the sizes differ, they are similar but not congruent.