Lks

133

Lampiran 3

LEMBAR KERJA SISWA (LKS)

No. 1

Mata Pelajaran : MatematikaSatuan Pendidikan : SMAKelas/Semester : XII/2Program : IPAPokok Bahasan : Trasformasi GeometriMateri Pelajaran : Translasi (pergeseran)Waktu : 20 menit

Kelompok:.....................Tanggal: ........................................

Indikator:1. Siswa dapat menentukan vektor translasi dari suatu titik yang

ditranslasikan ke bayangannya.2. Siswa dapat menentukan bayangan suatu titik oleh translasi tertentu.3. Siswa dapat menentukan suatu titik jika vektor traslasi dan bayangannya

diketahui

Petunjuk:

1. Diskusikan dengan teman kelompok kamu dan pahami dengan seksama

informasi pendukung yang terdapat dalam media pembelajaran mandiri,

jika ada kesulitan tanyakan kepada temanmu atau kepada guru. Untuk

menguji kemampuan kamu kerjakanlah soal – soal berikut.:

2. Sebelum mengerjakan tugas berikut pahami terlebih dahulu materi dan

animasi pada screen Translasi

134

1. Pergeseran titik A ke titik B dapat dituliskan dengan AB=( 6

−3).

Tuliskan komponen

pergeseran dari:

a. BC

b. CD

c. DE

d. EA

Jawaban:

a. BC = ...............................................

b. CD = ..............................................

c. DE = ...............................................

d. EA = ..............................................

2. Tentukan bayangan titik P (3, 7) jika ditranslasikan dengan translasi T =

(−3−4 )

!

Jawaban:

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................

A

B

CD

E

135

3. Suatu Pergeseran T=(a

b)menyebabkan titik A (3, 7) menjadi A’(-4, -1).

Tentukan nilai a dan b.

Jawaban:

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

............................................................................................................

4. Tentukan persamaan bayangan garis 2y – 3x + 5 = 0, jika dilakukan

translasi T=( 2−1).

Jawaban:

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

...............................................................................................................

136

LEMBAR KERJA SISWA (LKS)No. 2

Mata Pelajaran : MatematikaSatuan Pendidikan : SMAKelas/Semester : XII/2Program : IPAPokok Bahasan : Transformasi GeometriMateri Pelajaran : Pencerminan (refleksi)

a. Pencerminan terhadap sumbu Xb. Pencerminan terhadap sumbu Yc. Pencerminan terhadap garis y = xd. Pencerminan terhadap garis y = -xe. Pencerminan terhadap titik pangkal

koordinat.f. Pencerminan terhadap garis y = lg. Pencerminan terhadap garis x = k

Waktu : 20 menit

Kelompok: ........................ Tanggal: .......................

Indikator:1. Siswa dapat menentukan bayangan suatu titik/bangun oleh suatu

pencerminan.2. Siswa dapat menentukan bayangan suatu garis oleh suatu pencerminan.

Petunjuk:






animasi pada screen Pencerminan.

137

1. Gambarlah hasil pencerminan bangun-bangun berikut jika dicerminkan

terhadap garis yang digambarkan putus-putus!.

a. b.

2. Tentukan bayangan titik A (-2, 3), B (5, 2), C (6, 1) jika dicerminkan

terhadap:

a. sumbu Y

b. garis y = x

c. titik pangkal

Jawaban:

a. ..................................................................................................................

..................................................................................................................

..................................................................................................................

b. ..................................................................................................................

..................................................................................................................

..................................................................................................................

c. ..................................................................................................................

..................................................................................................................

..................................................................................................................

Y

X

Y

X

138

3. Tentukan bayangan garis 2x + 3y – 5 = 0 jika dicerminkan terhadap titik

pusat koordinat!.

Jawaban:

............................................................................................................

............................................................................................................

............................................................................................................

............................................................................................................

............................................................................................................

4. Tentukan bayangan trapesium ABCD dengan dengan A(3, 1), B(1, 3),

C(6, 4), dan D(5, 1), jika dicerminkan terhadap:

a. Garis y = 7

b. Garis x = 5

Jawaban:

a. ......................................................................................................

......................................................................................................

......................................................................................................

......................................................................................................

......................................................................................................

......................................................................................................

b. ......................................................................................................

......................................................................................................

139

......................................................................................................

......................................................................................................

......................................................................................................

......................................................................................................

5. Segitiga A’B’C’ adalah bayangan segitiga ABC oleh pencerminan garis x

= 5 dengan A’(6, 2), B’(4, 6) dan C’(2, 3), tentukan koordinat segitiga

ABC tersebut!.

Jawaban:

140


Mata Pelajaran : MatematikaSatuan Pendidikan : SMAKelas/Semester : XII/2Program : IPAPokok Bahasan : Transformasi GeometriMateri Pelajaran : Rotasi (perputaran)Waktu : 20 menit

Nama: ......................... Tanggal:....................... Kelompok: .....

Indikator:a. Siswa dapat menentukan bayangan suatu titik oleh rotasi dengan pusat O

(0, 0) sebesar b. Siswa dapat menentukan bayangan suatu titik oleh rotasi dengan pusat A

(a, b) sebesar .c. Siswa dapat menentukan bayangan suatu garis oleh rotasi dengan pusat (a,

b) sebesar

Petunjuk:






animasi pada screen rotasi

Tugas Kelompok

1. Tentukan banyangan titik A(5, 4), B(2, -1) dan C(3, 7) jika diputar dengan

pusat O sebesar:

a. 90o

141

b. -90o

c. 270o

Jawaban:

a. ..........................................................................................................

..........................................................................................................

..........................................................................................................

..........................................................................................................

..........................................................................................................

..........................................................................................................

....................................................................................................

b. ......................................................................................................

...................................................................................................

...................................................................................................

...................................................................................................

...................................................................................................

...................................................................................................

...................................................................................................

...................................................................................................

c. ...........................................................................................................

...........................................................................................................

142

...........................................................................................................

...................................................... ....................................................

...........................................................................................................

.......................................................

2. Tentukan bayangan titik P(2, 5) jika diputar sejauh 90o dengan pusat

putaran R(1, 1). Kemudian jelaskan dengan gambar!.

Jawaban:

............................................................................................................

............................................................................................................

............................................................................................................

............................................................................................................

............................................................................................................

....................................................................................

143

3. Tentukan bayangan garis x – 3y + 2 = 0 bila diputar 45o dengan pusat

A(1, -2).

Jawaban:

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

144

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

145


Mata Pelajaran : MatematikaSatuan Pendidikan : SMAKelas/Semester : XII/2Program : IPAPokok Bahasan : Transformasi GeometriMateri Pelajaran : Dilatasi Waktu : 20 menit

Nama: ......................... Tanggal: ....................... Kelompok: .........

Indikator:a. Siswa dapat menggambarkan hasil dilatasi suatu bangun oleh suatu dilatasi

dengan pusat (0, 0) dan faktor skala kb. Siswa dapat menentukan bayangan suatu titik dan menjelaskan dengan

gambar oleh suatu dilatasidengan pusat (a, b) dan faktor skala kc. Siswa dapat menentukan suatu transformasi tunggal yang mewakili

komposisi transformasi.d. Siswa dapat menentukan bayangan suatu garis jika dilakukan dua

trasformasi berurutan.e. Siswa dapat menentukan bayangan suatu titik jika titik tersebut mengalami

komposisi transformasi dengan terlebih dahulu menentukan transformasi tunggal yang mewakili komposisi transformasi.

Petunjuk:






animasi pada screen dilatasi dan komposisi transformasi

146

Tugas Kelompok

1. Gambarlah hasil dilatasi segitiga berikut dengan pusat dilatasi pada titik

pangkal koordinat dan faktor skala – 2

2. Diketahui titik A(3, 7) dan titik P(-1, 4). Tentukan bayangan titik A jika

dilakukan dilatasi [P, 2]. Kemudian jelaskan dengan gambar!.

Jawaban:

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

..........................................................................................

P

Q

R

Y

X

147

3. Suatu transformasi T 1=(2 1

1 3 ) dan

T 2=(−2 31 −2 )

, tentukan

transformasi tunggal yang mewakili komposisi transformasi:

a. T1 dilanjutkan dengan T2

b. T2 dilanjutkan dengan T1

Jawaban:

a. .................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

148

.................................................................................................................

.....................................................................................................

b. .................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

.....................................................................................................

4. Diketahui persamaan garis g:x + 2y + 3 = 0, tentukan persamaan bayangan

garis g jika ditraslasikan dengan dengan translasi T=(4

1 ) dilanjutkan

dengan pencerminan terhadap sumbu x.

Jawaban:

5. Tentukan koordinat bayangan titik A (6, -2) jika dirotasikan dengan pusat

O (0, 0) sebesar 270o dilanjutkan dengan transformasi T=(3 5

1 2 )dengan

terlebih dahulu menentukan transformasi tunggal sebagai wakil dari

komposisi dua transformasi.

Jawaban:

149

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

...................................................................................................................

150


Mata Pelajaran : MatematikaSatuan Pendidikan : SMAKelas/Semester : XII/2Program : IPAPokok Bahasan : Transformasi GeometriMateri Pelajaran : Komposisi TransformasiWaktu : 20 menit

Nama: ......................... Tanggal: ....................... Kelompok: .........

Indikator:a. Siswa dapat menentukan suatu transformasi tunggal yang mewakili

komposisi transformasi.b. Siswa dapat menentukan bayangan suatu garis jika dilakukan dua

trasformasi berurutan.c. Siswa dapat menentukan bayangan suatu titik jika titik tersebut mengalami

komposisi transformasi dengan terlebih dahulu menentukan transformasi tunggal yang mewakili komposisi transformasi.

Petunjuk:

Diskusikan dengan teman kelompok kamu dan pahami dengan seksama


jika ada kesulitan tanyakan kepada guru. Untuk menguji kemampuan

kamu kerjakanlah soal – soal berikut:

1. Suatu transformasi T 1=(2 1

1 3 ) dan

T 2=(−2 31 −2 )

, tentukan

transformasi tunggal yang mewakili komposisi transformasi:

c. T1 dilanjutkan dengan T2

d. T2 dilanjutkan dengan T1

Jawaban:

151

c. .................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

.....................................................................................................

d. .................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

.................................................................................................................

.....................................................................................................

2. Diketahui persamaan garis g:x + 2y + 3 = 0, tentukan persamaan bayangan

garis g jika ditraslasikan dengan dengan translasi T=(4

1 ) dilanjutkan

dengan pencerminan terhadap sumbu x.

Jawaban:

........................................................................................................................

........................................................................................................................

........................................................................................................................

152

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

...................................

3. Tentukan koordinat bayangan titik A (6, -2) jika dirotasikan dengan pusat

O (0, 0) sebesar 270o dilanjutkan dengan transformasi T=(3 5

1 2 )dengan

terlebih dahulu menentukan transformasi tunggal sebagai wakil dari

komposisi dua transformasi.

Jawaban:

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

........................................................................................................................

153

........................................................................................................................

....................................

Lks

Documents

Transcript of Lks