Congruency, Enlargement and Combined Transformations

Scale factor

The number k by which an enlargement multiplies lengths; areas multiply by k².

EnglishScale factor
Bahasa MelayuFaktor skala
中文比例因子

How it is used

A rectangle 3 cm by 4 cm is enlarged by scale factor k = 2, giving an image 6 cm by 8 cm. Its area grows from 12 cm² to 48 cm², that is 12 × k² = 12 × 4 = 48 cm².

Where it shows up in SPM

In enlargement questions in this Form 5 chapter. Paper 2 often gives object and image lengths and asks for k = image length ÷ object length, or gives k and an area and asks for the other area using the k² rule.

Paper 1 tests the length and area relationship.

Don't confuse it with

Area factorThe scale factor k multiplies lengths, but areas are multiplied by k², so a scale factor of 3 makes an area 9 times larger, not 3 times.

Open the chapter: Congruency, Enlargement and Combined Transformations →

Frequently asked questions

What does a negative scale factor mean?

A negative scale factor still changes the size by its number value, but the image is on the opposite side of the centre of enlargement and is turned upside down. For example k = −2 doubles the lengths and inverts the shape through the centre.

How do I find the scale factor from two shapes?

Divide a length on the image by the matching length on the object. If the image side is 10 cm and the object side is 4 cm, then k = 10 ÷ 4 = 2.5.

Use a pair of clearly corresponding sides to avoid mistakes.

Related terms

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