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Angle of Rotation

Arotationis atransformationin a plane that turns every point of a figure through a specified angle and direction about a fixed point.

The fixed point is called thecenter of rotation.

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

You can use aprotractorto 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.