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Triangle XYZ has vertices at X(−3, −3), Y(5, 5), Z(4, −6).

Part A: If triangle XYZ is rotated 90° clockwise about the origin, determine the coordinates of the vertices for the image, triangle X′Y′Z′. Show each step of your work. (4 points)

Part B: If triangle XYZ is rotated 270° counterclockwise about the origin, determine the coordinates of the vertices for the image, triangle X′Y′Z′. Show each step of your work. (4 points)

Part C: Describe the similarities and differences between the two rotations in parts A and B. (4 points)
(do only 2 sentences per part!!!!!!!!!!! and dumb it down a lot and make it seem like an 8th grader wrote it)

1 answer

Part A:

To rotate triangle XYZ 90° clockwise about the origin, we change the coordinates using the rule: (x, y) → (y, -x).

  1. For X(-3, -3):
    New coordinates = (-3, 3) → X' = (-3, 3)

  2. For Y(5, 5):
    New coordinates = (5, -5) → Y' = (5, -5)

  3. For Z(4, -6):
    New coordinates = (-6, -4) → Z' = (-6, -4)

So, the vertices of triangle X'Y'Z' are X'(-3, 3), Y'(5, -5), and Z'(-6, -4).

Part B:

To rotate triangle XYZ 270° counterclockwise about the origin, we use the rule: (x, y) → (-y, x).

  1. For X(-3, -3):
    New coordinates = (3, -3) → X' = (3, -3)

  2. For Y(5, 5):
    New coordinates = (-5, 5) → Y' = (-5, 5)

  3. For Z(4, -6):
    New coordinates = (6, 4) → Z' = (6, 4)

So, the vertices of triangle X'Y'Z' are X'(3, -3), Y'(-5, 5), and Z'(6, 4).

Part C:

The similarities are that both rotations moved the triangle around the origin, just in different directions. The differences are that the coordinates for each vertex changed differently, which means the shapes ended up in different places on the graph.