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△HIJ telah direfleksikan terhadap sumbu-x, kemudian sumbu-y, kemudian titik asal. Hasilnya refleksi berkoordinat di H   (4, 7), I   (10, −3), dan J   (−6, −8). Tentukan koordinat H, I, dan J.

Pertanyaan

begin mathsize 14px style triangle HIJ end style telah direfleksikan terhadap sumbu-undefined, kemudian sumbu-undefined, kemudian titik asal. Hasilnya refleksi berkoordinat di begin mathsize 14px style straight H apostrophe apostrophe apostrophe left parenthesis 4 comma space 7 right parenthesis end stylebegin mathsize 14px style straight I apostrophe apostrophe apostrophe left parenthesis 10 comma space minus 3 right parenthesis end style, dan begin mathsize 14px style straight J apostrophe apostrophe apostrophe left parenthesis negative 6 comma space minus 8 right parenthesis end style. Tentukan koordinat begin mathsize 14px style straight H end stylebegin mathsize 14px style straight I end style, dan begin mathsize 14px style straight J end style.

S. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

koordinat begin mathsize 14px style H left parenthesis 4 comma 7 right parenthesis comma space I left parenthesis 10 comma negative 3 right parenthesis comma space J left parenthesis negative 6 comma negative 8 right parenthesis end style.

Pembahasan

Diketahui refleksi begin mathsize 14px style triangle H I J end style adalah sebagai berikut:

begin mathsize 14px style triangle H I J rightwards arrow with s b minus x on top triangle H apostrophe I apostrophe J apostrophe rightwards arrow with s b minus y on top triangle H apostrophe apostrophe I apostrophe apostrophe J apostrophe apostrophe rightwards arrow with O left parenthesis 0 comma 0 right parenthesis on top triangle H apostrophe apostrophe apostrophe I apostrophe apostrophe apostrophe J apostrophe apostrophe apostrophe end style 

Apabila diketahui titik-titik hasil refleksi terakhir begin mathsize 14px style triangle H apostrophe apostrophe apostrophe I apostrophe apostrophe apostrophe J apostrophe apostrophe apostrophe end style dan kita ingin mendapatkan titik-titik awalnya, maka dapat dilakukan refleksi terhadap garis yang sama dengan sebelumnya, sehingga:

begin mathsize 14px style triangle H apostrophe apostrophe apostrophe I apostrophe apostrophe apostrophe J apostrophe apostrophe apostrophe rightwards arrow with O left parenthesis 0 comma 0 right parenthesis on top triangle H apostrophe apostrophe I apostrophe apostrophe J apostrophe apostrophe rightwards arrow with s b minus y on top triangle H apostrophe I apostrophe J apostrophe rightwards arrow with s b minus x on top triangle H I J end style

Kita ketahui rumus refleksi titik begin mathsize 14px style left parenthesis a comma b right parenthesis end style terhadap:

- titik asal begin mathsize 14px style O left parenthesis 0 comma 0 right parenthesis rightwards arrow left parenthesis a apostrophe comma b apostrophe right parenthesis equals left parenthesis negative a comma negative b right parenthesis end style  
- sumbunegative y size 14px rightwards arrow size 14px left parenthesis size 14px a size 14px apostrophe size 14px comma size 14px b size 14px apostrophe size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px minus size 14px a size 14px comma size 14px b size 14px right parenthesis 
- sumbusize 14px minus size 14px x size 14px rightwards arrow size 14px left parenthesis size 14px a size 14px apostrophe size 14px comma size 14px b size 14px apostrophe size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px a size 14px comma size 14px minus size 14px b size 14px right parenthesis  

Sehingga:

Refleksi ketiga (terhadap titik asal undefined):
 begin mathsize 14px style H apostrophe apostrophe apostrophe left parenthesis 4 comma 7 right parenthesis rightwards arrow H apostrophe apostrophe left parenthesis negative 4 comma negative 7 right parenthesis I apostrophe apostrophe apostrophe left parenthesis 10 comma negative 3 right parenthesis rightwards arrow I apostrophe apostrophe left parenthesis negative 10 comma 3 right parenthesis J apostrophe apostrophe apostrophe left parenthesis negative 6 comma negative 8 right parenthesis rightwards arrow J apostrophe apostrophe left parenthesis 6 comma 8 right parenthesis end style 

Refleksi kedua (terhadap sumbubegin mathsize 14px style negative y end style)
begin mathsize 14px style H apostrophe apostrophe left parenthesis negative 4 comma negative 7 right parenthesis rightwards arrow H apostrophe left parenthesis 4 comma negative 7 right parenthesis I apostrophe apostrophe left parenthesis negative 10 comma 3 right parenthesis rightwards arrow I apostrophe left parenthesis 10 comma 3 right parenthesis J apostrophe apostrophe left parenthesis 6 comma 8 right parenthesis rightwards arrow J apostrophe left parenthesis negative 6 comma 8 right parenthesis end style

Refleksi pertama (terhadap sumbubegin mathsize 14px style negative x end style)
size 14px H size 14px apostrophe size 14px left parenthesis size 14px 4 size 14px comma size 14px minus size 14px 7 size 14px right parenthesis size 14px rightwards arrow size 14px H size 14px left parenthesis size 14px 4 size 14px comma size 14px 7 size 14px right parenthesis size 14px I size 14px apostrophe size 14px left parenthesis size 14px 10 size 14px comma size 14px 3 size 14px right parenthesis size 14px rightwards arrow size 14px I size 14px left parenthesis size 14px 10 size 14px comma size 14px minus size 14px 3 size 14px right parenthesis size 14px J size 14px apostrophe size 14px left parenthesis size 14px minus size 14px 6 size 14px comma size 14px 8 size 14px right parenthesis size 14px rightwards arrow size 14px J size 14px left parenthesis size 14px minus size 14px 6 size 14px comma size 14px minus size 14px 8 size 14px right parenthesis

Jadi koordinat begin mathsize 14px style H left parenthesis 4 comma 7 right parenthesis comma space I left parenthesis 10 comma negative 3 right parenthesis comma space J left parenthesis negative 6 comma negative 8 right parenthesis end style.

1rb+

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