How to Solve Rotation Maths


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:


    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:


    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)


  • Photo Credit Kolyasha/iStock/Getty Images
Promoted By Zergnet



You May Also Like

  • How to Calculate Specific Rotation of a Sample

    Solutions of chemical compounds rotate light rays differently. Chemists identify substances observing the direction and extent to which they rotate plane-polarized rays....

  • How to Rotate HTML Text 90 Degrees

    The standard for cascading style sheets, CSS3, introduced the transform property that makes it easy to rotate text to any degree angle,...

  • How to Find Time With Kinematic Equations

    One of the most important applications of physics is the ability to predict the future movement of an object based on past...

  • How to Rotate a Triangle on a Grid

    Two-dimensional rotations come up often in digital image production and game programming. As objects move around in a virtual world they can...

  • How to Teach Transformations for Math

    In geometry, transformations relate to the movement of figures on a plane. Teach students the procedures of various transformations by practicing them,...

  • How to Make Rotation Tessellations

    Tessellations are geometric patterns that repeat without any breaks to form a larger design. While tessellations are studied in mathematics, artists and...

  • Different Kinds of Symmetries in Math

    There are four types of symmetries in the mathematics of plane geometry: reflection, rotation, translation, and glide reflection. An object is said...

Related Searches

Check It Out

How to Build and Grow a Salad Garden On Your Balcony

Is DIY in your DNA? Become part of our maker community.
Submit Your Work!