Pertanyaan

Tentukan bayangan garis ≡ y = 2 x + 2 jika dirotasi sejauh 4 5 ∘ dengan pusat ( 0 , 0 ) .

Tentukan bayangan $garis \equiv y = 2 x + 2$ jika dirotasi sejauh $4 5^{\circ}$ dengan pusat $(0, 0)$ .

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Jawaban

bayangan garis adalah .

bayangan garis adalah 3 over 2 square root of 2 x apostrophe plus 1 half square root of 2 y apostrophe plus square root of 2 equals 0

Pembahasan

Gunakan persamaan matriks berikut: Menentukan persamaan bayangan dengan cara invers matriks: diperoleh , substitusikan persamaan garis . Jadi, bayangan garis adalah .

Gunakan persamaan matriks berikut:

Menentukan persamaan bayangan dengan cara invers matriks:

$open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses equals open parentheses table row cell 1 half square root of 2 end cell cell negative 1 half square root of 2 end cell row cell 1 half square root of 2 end cell cell 1 half square root of 2 end cell end table close parentheses open parentheses table row x row y end table close parentheses open parentheses table row x row y end table close parentheses equals open parentheses table row cell 1 half square root of 2 end cell cell negative 1 half square root of 2 end cell row cell 1 half square root of 2 end cell cell 1 half square root of 2 end cell end table close parentheses to the power of negative 1 end exponent open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses open parentheses table row x row y end table close parentheses equals fraction numerator 1 over denominator open parentheses 1 half square root of 2 close parentheses open parentheses 1 half square root of 2 close parentheses minus open parentheses negative 1 half square root of 2 close parentheses open parentheses 1 half square root of 2 close parentheses end fraction open parentheses table row cell 1 half square root of 2 end cell cell 1 half square root of 2 end cell row cell negative 1 half square root of 2 end cell cell 1 half square root of 2 end cell end table close parentheses open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses open parentheses table row x row y end table close parentheses equals fraction numerator 1 over denominator begin display style 1 half plus 1 half end style end fraction open parentheses table row cell 1 half square root of 2 end cell cell 1 half square root of 2 end cell row cell negative 1 half square root of 2 end cell cell 1 half square root of 2 end cell end table close parentheses open parentheses table row cell x apostrophe end cell row cell y apostrophe end cell end table close parentheses open parentheses table row x row y end table close parentheses equals open parentheses table row cell 1 half square root of 2 x apostrophe plus 1 half square root of 2 y apostrophe end cell row cell negative 1 half square root of 2 x apostrophe plus 1 half square root of 2 y apostrophe end cell end table close parentheses open parentheses table row x row y end table close parentheses equals 1 half square root of 2 open parentheses table row cell x apostrophe plus y apostrophe end cell row cell negative x apostrophe plus y apostrophe end cell end table close parentheses$

diperoleh x equals 1 half square root of 2 open parentheses x apostrophe plus y apostrophe close parentheses space dan space y equals 1 half square root of 2 open parentheses negative x apostrophe plus y apostrophe close parentheses , substitusikan persamaan garis y equals 2 x plus square root of 2 .

Jadi, bayangan garis adalah 3 over 2 square root of 2 x apostrophe plus 1 half square root of 2 y apostrophe plus square root of 2 equals 0 .