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Algebra

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I'm stuck!! Can someone please help me with this problem??

A triangle has vertices (1, 4), (1, 1), and (-3, 1). The triangle is dilated by a scale factor of 2, then translated 5 units up, and then rotated 90 degrees counterclockwise about the origin. What are the vertices of the image of the triangle?

  • Algebra - ,

    dilate by 2: (x,y) -> (2x,2y)
    up 5: (x,y) -> (x,y+5)
    rotate: (x,y) -> (-y,x)
    combining them,

    (x,y) -> (2x,2y) -> (2x,2y+5) -> (-(2y+5),2x)

    so,

    (1,4) -> (-13,2)
    and so on for the other points

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