transformasi geometri

1.

translasi T(a,b)

x' = x + a → x = x' - a

y' = y + b → y = y' - b

•

T(3,-4)

a = 3

b = -4

bayangan garis

3x - 2y = 6

3(x' - a) - 2(y' - b) = 6

3(x' - 3) - 2(y' + 4) = 6

3x' - 9 - 2y' - 8 = 6

3x' - 2y' = 6 + 9 + 8

3x - 2y = 23

#caracepat

T(a,b) = (3,-4)

bayangan garis

3x - 2y = 6 + 3a - 2b

3x - 2y = 6 + 9 + 8

3x - 2y = 23

2.

dilatasi [A,k]

A = pusat dilatasi = (a,b)

k = faktor skala

•

D[A(-2,1) , k = 1/2]

a = -2

b = 1

P(12,-5) → P'(x' , y')

x' = k(x - a) + a

x' = 1/2 (12 - (-2)) + (-2)

x' = 1/2 × 14 - 2

x' = 7 - 2

x' = 5

y' = k(y - b) + b

y' = 1/2 (-5 - 1) + 1

y' = 1/2 × (-6) + 1

y' = -3 + 1

y' = -2

bayangan P = P'(x' , y') → P'(5,-2)