Construction

Performing a Rotation

Rotations can be performed by hand with the help of a straightedge, a compass, and a protractor.

To rotate point A about point P by an angle of 130^(∘) measured counterclockwise, follow these five steps.

Draw PA

Using the straightedge, draw the segment connecting the center of rotation P and point A.

Place the Protractor

Place the center of the protractor on P and align it with PA.

The protractor is placed as illustrated above when the rotation is counterclockwise. If the rotation has to be done clockwise, the protractor needs to be placed as follows.

Mark the Desired Angle

Locate the corresponding measure on the protractor and make a small mark. In this case, the mark will be made at 130^(∘).

Draw a Ray

Using the straightedge, draw a ray with starting point P that passes through the mark made in the previous step.

Drawing a Ray starting a P that makes a 130 degree angle with segment PA

Draw Point A'

Place the compass tip on P and open it to the distance between P and A. Without changing this setting and keeping the point of the compass at P, draw a small arc centered at P that intersects the ray drawn before.

Measuring PA with the compass and making an arc that intersects the ray drawn before

The intersection of the ray and the arc is the image A' after the give rotation.

Notice that this method of construction has also confirmed that PA is congruent to PA'.

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