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Angle of Rotation

A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point.

The fixed point is called the center of rotation .

The amount of rotation is called the angle of rotation and it is measured in degrees.

You can use a protractor to measure the specified angle counterclockwise.

Consider the figure below.

Here, Δ A ' B ' O is obtained by rotating Δ A B O by 180 ° about the origin. Observe that both A O A ' and B O B ' are straight lines.

So, m A O A ' = 180 ° = m B O B ' .

Example:

How many degrees has the Δ X Y Z been rotated counterclockwise to obtain the Δ X ' Y ' Z ' ?

A . 90 ° B . 180 ° C . 270 ° D . 360 °

Identify the corresponding vertices of the rotation.

X ( 6 , 2 ) X ' ( 2 , 6 ) Y ( 2 , 4 ) Y ' ( 4 , 2 ) Z ( 4 , 5 ) Z ' ( 5 , 4 )

The point of rotation is the origin, draw lines joining one of the points, say X and it's image to the origin.

You can see that the lines form an angle of 270 ° , in the counterclockwise direction.

Therefore, Δ X ' Y ' Z ' is obtained by rotating Δ X Y Z counterclockwise by 270 ° about the origin.

So, the correct choice is C .

Also note that the relation between the corresponding vertices is ( x , y ) ( y , x ) which shows a counterclockwise rotation of 270 ° about the origin.