Algebra

posted by .

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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. MATH

    A triangle with the vertices A(–3, 4), B(3, 1), and C(–1, –5) is dilated by a scale factor of 2. Find the coordinates of A', B', and C'.
  2. geometry

    I realy need help please!!!! 1-Describe the translation in words: (x, y) (x - 4, y - 9) A)4 units to the left, 9 units down B)4 units to the left, 9 units up C)4 units to the right, 9 units down D)4 units to the right, 9 units up 2-][3-,2.[1,4],[-5,4]2,-3]at …
  3. Algebra

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

    A triangle has vertices with coordinates (2, 0), (3, -1), and (-2, -5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image.
  5. math

    A triangle has vertices with coordinates (2, 0), (3, -1), and (-2, -5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image.
  6. Matrices

    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° counterclockwise about the origin. What are the vertices of the image of the …
  7. Math

    A triangle has vertices at S(1, 1), T(2, -3) and U(4, 0). The triangle is translated up 3 units. What are the coordinates of the vertices of the image?
  8. Math

    a triangle has vertices at S(1,1), T(2, -3) and U(4, 0). the triangle is translated up 3 units. what are the coordinates of the vertices of the image?
  9. 8th Grade Pre-Algebra

    Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(3, −6), Q(0, 9), and R(−3, 0). Triangle P'Q'R' has vertices P'(1, −2), Q'(0, 3), and R'(−1, 0). Plot triangles PQR and P'Q'R' on your own coordinate …
  10. math

    A triangle has vertices at S(4,1), T(2,-3),and U(4,0). The triangle is translated up 3 units. What are the coordinates of the vertices of the image?

More Similar Questions