Congruency, Enlargement and Combined Transformations · 5.3.3
Describing combined transformations
Students state, with full detail, the two transformations (in the correct order) that together map an object onto a given final image. This includes naming each transformation's type and giving all necessary details, mirror line, centre and angle of rotation, translation vector, or centre and scale factor of enlargement.
The official learning standard (5.3.3)
“Describe combined transformation.”
What it means
Students state, with full detail, the two transformations (in the correct order) that together map an object onto a given final image. This includes naming each transformation's type and giving all necessary details, mirror line, centre and angle of rotation, translation vector, or centre and scale factor of enlargement.
How it is examined
Paper 2 commonly shows an object and its final image (on a grid or via coordinates) after two transformations, and asks students to describe each transformation in the order performed, with all details correct for full marks.
Worked example
Point K(3, 2) is mapped to point K′(3, −2) by transformation V, and then K′ is mapped to point K″(3, 5) by transformation W. Describe transformation V and transformation W, hence describe the combined transformation that maps K to K″.
- Compare K(3, 2) and K′(3, −2): the x-coordinate is unchanged and the y-coordinate is negated, so V is a reflection in the x-axis.
- Compare K′(3, −2) and K″(3, 5): the x-coordinate is unchanged and the y-coordinate increases by 7 (from −2 to 5), so W is a translation by the vector (0, 7).
- The combined transformation that maps K directly to K″ is V followed by W.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What details must I include when describing a transformation?
State the type of transformation, then all relevant details: for a translation give the vector, for a reflection give the equation of the mirror line, for a rotation give the centre, angle and direction, and for an enlargement give the centre and scale factor.
How do I identify each transformation just from coordinates?
Compare the object's and image's coordinates. Equal x with negated y suggests reflection in the x-axis; equal y with negated x suggests reflection in the y-axis; a constant shift added to both coordinates suggests a translation by that vector.
Does the order in which I state the two transformations matter?
Yes. State them in the order they actually happened, since swapping the order can produce a different image, combined transformations generally do not commute, so the order carries real mathematical meaning, not just wording.