1. The document provides examples of transformations of lines under compositions of transformations. 2. It gives the equations of the image of lines g and h under the transformations Mg(h) and Mh(g) for different lines g and h. 3. It also finds the equations of the image of lines g, h, and k under various transformations Mg, Mh, and their compositions.

1. LATIHAN SOAL HASIL KALI TRANSFORMASI
1. Diketahui garis g = { (x,y )| x + 2y = 1 }dan h = {(x,y )| x = -1 }.Tulislah
sebuah persamaan garis g1 Mg(h).
Penyelesaian :
g {( x.y) | x + 2y = 1} dan h = { (x ,y ) | x = -1 }
g = x + 2y = 1 h = x = -1
x = 0 y = 2
y = 0 x = 1
X = -1 X + 2y = 1
h = -1
g = x + 2y = 1
( -1 ) + 2y = 1
2y = 2
y = 1
2. Diketahui garis g = { (x , y) | 3x – y + 4 = 0 } dan garis h = { (x, y ) | y=
2}. Tulislah persamaan garis g’= M h (g).
Penyelesaian :
g = { x,y ) | 3x – y + 4 =0 dan garis h = { ( x,y ) | y =2 }
h = y = 2
g 3x y 4 0
M h (g ) g
3x – 2y + 4=0
3x – 2 garis persamaan yang di maksud yaitu g = { ( x,y ) | y = 1 }
3. Diketahui garis –garis g = { (x,y) | y = 0 },h = { (x,y) | y = x } dan k ={
(x,y) | x =2}
Tulislah persamaan garis – garis berikut :
a) M g (h) b) M h (g)
c) M g (g)
Penyelesaian :
Diketahui
g = { (x,y) | y = 0 }
h = { (x,y) | y = x }

2. k ={ (x,y) | x = 2 }
a) M g (h) = y = x
0 = x
x= 0
Jadi persamaan yang di maksud { ( x,y ) | x =0 }
b) M h (k) x 2
y = 0
c) M g (g) = y = 0
4) Diketahui garis – garis g dan h dan titik – titik P dan Q
Lukislah :
a) A = M g [M h ( p)]
b) B =M h [M g ( p)]
c) C = M h [M h ( p)]
d) D =M h [M h (k )]
e) R Sehingga M g [M h( R )] Q
f) Apakah M g oM h= M h oM g ?mengapa ?
Penyelesaian :
a) A = M g [M h ( p)]
M h( p)= P’
M h (p)= A
b) B =M h [M g ( p)]
M g(p)= p”
M h( p)= B
c) C = M h [M h ( p)]
M h (p)= p‘
M h (p)= C

3. d) D =M h [M h (k )]
M h (k)= k’
M h (k)= =k= K‘=D
e) M h[M g(R)] = Q
M h [M g( R)] Q
M g (R)= R’
M h (R)= Q
f) M g oM h M(h)oM g
karena :
A = M g [M h (P)]
M h (p)= p’
M g( p)= p’
B=M h [M g (P)]
M g (p)= p”
M h (p)= B