Math Problem Statement
Sebuah persamaan garis 2x + y + 3 = 0 2x + y + 3 = 0 dirotasikan dengan pusat O(0,0) sebesar 90° 90° berlawanan dengan arah putaran jarum jam kemudian didilatasi dengan pusat O (0,0) dan faktor skala k = 3 maka bayangan garis tersebut adalah....
Select one:
a. - x + 2y + 9 = 0 - x + 2y + 9 = 0
b. 2x-2y+902x-2y + 9 = 0
c. 2x-y+3=02x-y+3 = 0
d. - 2x + y + 9 = 0 - 2x + y + 9 = 0
e. 2x+y-3=02x+y-3=0
Solution
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Math Problem Analysis
Mathematical Concepts
Analytic Geometry
Rotation of Lines
Dilation
Formulas
Rotation formula: (x', y') = (-y, x) for 90° counterclockwise
Dilation formula: (x', y') = (kx, ky) where k is the scale factor
Theorems
Rotation Theorem: A point rotated around the origin by 90° counterclockwise transforms (x, y) to (-y, x)
Dilation Theorem: Dilation with respect to the origin multiplies each coordinate by the scale factor k
Suitable Grade Level
Grades 10-12
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