The important formulas of Transformation as listed below:-
1. reflection in X-axis: P(a, b) = p’(a, – b)
2. reflection in Y-axis : P(a, b) = p’(- a, b)
3. reflection in Y = X[W]: P(a, b) = P’(b, a)
4. reflection in Y = X[Z]: P(a, b) = P’(- b, a)
5. reflection in X = h[R]: P(a, b) = P’(2h – a, b)
6. reflection in Y = K[M]: P(a, b) = P’(a, 2k – b)
7. positive quarter turn about O[Q]: P(a, b) = P’(- b, a)
8. negative quarter turn about
9. half turn about O[H]: P(a, b) = P’(-a, – b)
10. translation with
11. enlarging at O with scale factor K[E]: P(a, b) = P’(ka, kb)
12. enlarging at P with a scale factor K: P(a, b) = P’(ka + x, kb + y)
13. enlargement with centre at C (x, y) and K as scale factor denoted by E (c, k); P(a, b) = P’[x + k (a – x), y + k(b – y)]
14. the scale factor
15. rotation P(a, b) about centre
C (x, y) by -90 = P’(b + x – y, -a + x +y)
16. rotation P(a, b0 about centre
C(x, y) by +90 = P’ (-a + x +y, a – x + y)
17. rotation P(a, b) about centre
C(x, y) by 180 = p’(2x – y, 2y – b)
18. combination of transformation:
i. if Q = positive turn about the origin & W is the reflection in the line y = x, then QW = Y where Y is the reflection in Y-axis.
ii. where H is the half turn about O.
iii. WQ = X where X is the reflection in the X-axis
iv. where I is the identity transformation.
v. where is the negative quarter turn about O.
vi. where Z is the reflection in Y = X axis.
vii. XH = Y
viii. YH = X
ix. XY = H
x. HYX = 1
TRANSFORMATION USING MATRICES:
I. represents reflection in X-axis.
II. represent identity transformation.
III. represents reflection in Y-axis.
IV. represents reflection in the line Y = X.
V. represents reflection in the line Y = -X.
VI. represent positive quarter turn about the origin.
VII. represents negative quarter turn about the origin.
VIII. represents half turn about origin.
IX. represents the enlargement with centre at the origin and scale factor k.
X. The 2 * 1 matrix represents translation through ‘a’ units along X-axis and ‘b’ units along Y-axis.
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