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Algebra

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I need help with two math problems.

1. 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?

2. Use matrices to solve the system.
2x+3y=4
5x+8y=11

I appreciate the help!

  • Algebra -

    1.
    The transformations are:
    e(O,2) : dilation about origin of 2 units
    t(0,5) : translation 5 units up
    r(y,-x) : rotation counter-clockwise 90°

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

    So combining it all:
    (x,y) -> (2y+5, -2x)

    2.
    Using Cramer's rule:
    Δ=8*2-3*5=1
    x=(4*8-11*3)/Δ=-1
    y=(2*11-5*4)/Δ=2
    Check:
    2(-1)+3*2=4
    5(-1)+8*2=11
    ok.

  • Algebra -

    I'm still confused on the first one. Thank you. I appreciate it.

  • Algebra -

    I need help

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