Question

Simple answers please
A carousel is represented in a coordinate plane with the center of the carousel at the origin. You and three friends sit at A(-4, -4), B (-3, 0), C (-1, -2), and D (-2, -3). At the end of the ride, your positions have rotated 270° clockwise about the center of the carousel. What are your locations at the end of the ride?

A:

B:

C:

D:

Answers

  1. Answer:
    • A'(4, -4)
    • B'(0, -3)
    • C'(2, -1)
    • D'(3, -2)
    Step-by-step explanation:
    The coordinate transformation for a 270° clockwise rotation is the same as for a 90° counterclockwise rotation:
      (x, y) ⇒ (-y, x)
    The rotated points are …
      A(-4, -4) ⇒ A'(4, -4)
      B(-3, 0) ⇒ B'(0, -3)
      C(-1, -2) ⇒ C'(2, -1)
      D(-2, -3) ⇒ D'(3, -2)
    _____
    Additional comment
    To derive and/or remember these transformations, it might be useful to consider where a point came from when it ends up on the x- or y-axis.
    A point must have come from the -y axis if rotating it 270° CW makes it end up on the +x-axis. A point must have come from the x-axis if rotating it 270° makes it end up on the +y axis. That is why we write …
      (x, y) ⇒ (-y, x) . . . . . . the new x came from -y; the new y came from x

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