10.1 Transformations II
10.1.1 Similarity
Two shapes are similar if
(a) the corresponding angles are equal and
(b) the corresponding sides are proportional.
Example:
Quadrilateral ABCD is similar to quadrilateral JKLM because
∠A=∠J=90o∠B=∠K=50o∠C=∠L=130o∠D=∠M=90o
(All the corresponding angles are equal.)
ABJK=510=12BCKL=48=12CDLM=2.55=12ADJM=36=12
(All the corresponding sides are proportional.)
10.1.2 Enlargement
1. Enlargement is a type of transformation where all the points of an object move from a fixed point at a constant ratio.
2. The fixed point is known as the centre of enlargement and the constant ratio is known as the scale factor.
Scale factor=length of side of imagelength of side of object
3. The object and the image are similar.
4. If A’ is the image of A under an enlargement with centre O and scale factor k, then
OA'
- if k > 0, then the image is on the same side of the object.
- if k < 0, then the image is on the opposite side of the object.
- if –1 < k < 1, then the size of the image is a reduction of the size of the object.
5. Area of image = k2 × area of object.