Jika Titik C(-7,5) dirotasikan sejauh 90° searah jarum jam dengan pusat O(0,0) kemudian ditranslasikan T= 3 −4 , maka bayangannya adalah …. (-3,8) (-8,3) (8,-3) (8,3) (-8,-3)

Mathematics

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Step-by-step solution

2 steps
  1. Perform the rotation of point C(-7,5) 90° clockwise around the origin O(0,0).

    A rotation of 90° clockwise around the origin transforms a point (x,y)(x,y) to (y,−x)(y, -x).
    For C(-7,5):

    C′=(5,−(−7))C' = (5, -(-7)) C′=(5,7)C' = (5, 7)
  2. Perform the translation on the rotated point C'(5,7).

    The translation vector is T=(3−4)T = \begin{pmatrix} 3 \\ -4 \end{pmatrix}.
    A translation by vector (ab)\begin{pmatrix} a \\ b \end{pmatrix} transforms a point (x,y)(x,y) to (x+a,y+b)(x+a, y+b).
    For C'(5,7) and T=(3−4)T = \begin{pmatrix} 3 \\ -4 \end{pmatrix}:

    C′′=(5+3,7+(−4))C'' = (5 + 3, 7 + (-4)) C′′=(8,7−4)C'' = (8, 7 - 4) C′′=(8,3)C'' = (8, 3)

    The final image of the point is (8,3).

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