How to Solve Rotation Maths

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A common problem within geometry involves rotating a shape -- described by a set of points -- about the origin by a fixed number of degrees and then trying to calculate the new position of the points. Rotation problems can be solved with a simple set of rules.

Things You'll Need

  • Graph paper
  • Tracing paper
  • Colored Pencils
  • Compass
  • Using the graph paper, draw a linear graph and label the horizontal axis "x" and the vertical axis "y." Plot the coordinate of your shape onto the graph. For this example, lets assume the shape is a rectangle with points:

    (-4,2)
    (4,2)
    (4,-2)
    (-4,-2)

    Use lines to connect successive points.

  • Place the tracing paper over the graph paper and use the compass to fix the axis of rotation to the graph origin (0,0). On the tracing paper, trace over the points that have been plotted upon the underlying graph paper.

  • Rotate the tracing paper by the rotation amount required. For the sake of this example, we will assume the tracing paper has been rotated 90 degrees about the origin. You should now be able to see the new coordinates of each of the points. Following the example, the new points of the rectangle are:

    (-2,4)
    (2,4)
    (2,-4)
    (-2-4)

    Write down each of these points and remove the tracing paper. Plot the new points on the graph paper using a pencil of a different color. Connect the successive points with lines. The rotation has been completed.

  • Notice that when you rotate a set of points by 90 degrees, you simply change the order and sign of the coordinates. If we have coordinates (-4,2) then this has changed to (2,4). Generally speaking, if we have a point (A,B) then rotating by 90 degrees changes the point to (-B,A).

    Similar rules can be stated for 180-degree rotations and 270-degree rotations:

    180 degree rotation: (A,B) --> (-A,-B)

    270 degree rotation: (A,B) --> (B,-A)

References

  • Photo Credit Kolyasha/iStock/Getty Images
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