10.1 Transformations II


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=90oB=K=50oC=L=130oD=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.