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 = 90 o B = K = 50 o C = L = 130 o D = M = 90 o
(All the corresponding angles are equal.)

A B J K = 5 10 = 1 2 B C K L = 4 8 = 1 2 C D L M = 2.5 5 = 1 2 A D J M = 3 6 = 1 2
(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 image length 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 O A ' O A = k
  • 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.

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