3.1b Determining the Image of an Object under Combination of (a) Two Enlargements or (b) an Enlargement and an Isometric Transformation
1. Enlargement is a transformation where all points of an object on a plane move from a fixed point at a constant ratio.
2. The fixed point is called the centre of enlargement and constant ratio is called the scale factor.
Scale factor,k =Length of image sideLength of object side
Scale factor,k =Length of image sideLength of object side
3. For enlargement, the object and the image are similar.
4. Area of image = (Scale factor)2 × Area of object
= k2 × Area of object
Example:
E, P and T are three transformations that are defined as follows:
E = Enlargement with centre V (0, –1) and a scale factor of 2.
P = Reflection at the line y = –1.
T =
T =
Based on the diagram above, determine the image of the shaded figure under the combined transformations
(a) E2 (b) ET (c) EP
Solution:
(a)
Shaded figure → (E) figure III → (E) figure D.
Hence, the image of the shaded figure under the combined transformation E2 = EE is the figure D.
(b)
Shaded figure → (T) figure II → (E) figure A.
Hence, the image of the shaded figure under the combined transformation ET is the figure A.
(c)
Shaded figure → (P) figure I → (E) figure B.
Hence, the image of the shaded figure under the combined transformation EP is the figure B.