How to Rotate a Triangle on a Grid

Written by jenna meeks
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How to Rotate a Triangle on a Grid
Rotating shapes on a grid requires knowing the rules for each rotation (Jupiterimages/BananaStock/Getty Images)

Transformations are a common topic covered in algebra class. Of the four basic transformations, translations, dilations, reflections and rotations, rotations can be the hardest to figure out how to do. There are three ways in which you could be asked to rotate a shape on a grid, 90 degrees clockwise, 90 degrees counterclockwise, or 180 degrees. These operations are not as difficult as they look if you know how to to change the points around.

Skill level:
Moderate

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Things you need

  • Graph paper
  • 2 colours of pen or pencil

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Instructions

    Rotate 90 Degrees Clockwise

  1. 1

    Draw your triangle on the graph paper, make sure you write the coordinates for each of the three points.

  2. 2

    Take each coordinate and switch the "x" and the "y". For example, (3, 4) would become (4,3).

  3. 3

    Make all of the new y-coordinates negative of what they were. For example (4,3) would become (4,-3), but (5,-2) would become (5,2).

  4. 4

    Plot the new points on the graph in a different colour of pen or pencil.

  5. 5

    Connect the points with straight lines to draw your rotated triangle.

    Rotate 90 Degrees Counterclockwise

  1. 1

    Graph your original triangle. Be sure to note the coordinates of the three points.

  2. 2

    Switch the "x" and "y" coordinates for each point. For example (7, 2) becomes (2, 7).

  3. 3

    Make the new x-coordinates for all of your points negative. For example, (2, 7) becomes (-2, 7), but (-3, 6) would become (3, 6).

  4. 4

    Plot the three new points on your graph in a different colour from the one you drew the first triangle in.

  5. 5

    Connect the points with three straight lines, and you have drawn your rotated triangle.

    Rotate 180 Degrees

  1. 1

    Graph your original triangle on a coordinate plane in your graph paper. Be sure to make note of the coordinates of the three points of the triangle.

  2. 2

    Take each of the three points and make both the x and y-coordinates negative. For example, (9, 3) would become (-9, -3), but (-4, -5) would become (4, 5), and (-7, 2) would become (7, -2).

  3. 3

    Plot your new points on the graph in a different colour from the original triangle.

  4. 4

    Draw three straight line to connect the points and you have your new rotated triangle.

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