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anonymous

  • one year ago

ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin. It is then reflected across the line y = -x. What are the coordinates of the vertices of the image? A. A'(0, 3), B'(2, 3), C'(1, 1) B. A'(0, -3), B'(3, -2), C'(1, -1) C. A'(-3, 0), B'(-3, 2), C'(-1, 1) D. A'(0, -3), B'(-2, -3), C'(-1, -1)

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  1. mathmate
    • one year ago
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    Hints: Rotation \(R_{180}: (x,y)\rightarrow (-x,-y)\) Reflection \(S_{y=-x}:(x,y)\rightarrow (-y,-x)\) Transform separately, or combine them: \(S_{y=-x}\circ R_{180}: (x,y)\rightarrow (y,x)\equiv S_{y=x}\) For example, Point (7,1) after rotation of 180 becomes (-7,-1) followed by a reflection about y=-x gives (1,7) as the final position. Alternatively, using a single reflection about y=x also transforms from (7,1) to (1,7), as explained above.

  2. anonymous
    • one year ago
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    So Its B?

  3. mathmate
    • one year ago
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    I don't usually work with letters. I will be glad to confirm if you post the values represented by option "B".

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