The different kinds of transformations include translation,
reflection, and rotation. You have already learned how use
translations to shift objects on a coordinate plane both
horizontally and vertically. You have also reflected objects over
mirror lines. Now, it is time to learn about rotations.
In the slideshow below, you will learn about rotating objects in
the coordinate plane, including the vocabulary you need to
understand.
What is a rotation?
Rotation is the circular movement of
an object around a fixed point in the coordinate plane
called the center of rotation. The
center of rotation is an ordered pair in the
coordinate plane. The most common center of rotation
is
\(\left(0,0\right)\), but you can rotate an object around any point in
the plane. A rotated image and its preimage are
congruent.
To rotate an object in the coordinate plane, you need
to know the degree of rotation. This
is the angle measure, in degrees, that the object will
be rotated. It tells you how many degrees to rotate
the object.
Which represents a center of rotation:
\(\left(0,0\right)\)
or
\(90^\circ\)?
The point
\(\left(0,0\right)\)
represents a center of rotation because it is an
ordered pair. A center of rotation is always an
ordered pair. The measure
\(90^\circ\)
represents a degree of rotation.
Counterclockwise and Clockwise Rotation
When rotating an object in the coordinate plane, you
need to know the center of rotation and the degree of
rotation. Since rotation is a circular motion, so you
also need to know the direction in which to rotate the
object. There are two options: counterclockwise and
clockwise.
The table below explains the difference between these
two motions. Read the description of the motion in the
column on the left, and then click to see the motion
in the column on the right.
The arrows show counterclockwise movement
on the plane.
The arrows show clockwise movement on the
plane.
Mathematical Notation for Rotations
To rotate an object in the coordinate plane, you need
to know the center of rotation, the degree of
rotation, and the direction of rotation. This is a lot
of information to keep track of! Fortunately, you can
use mathematical notation to help.
Rotation Notation
\(R_{degrees}\)
represents a rotation of a specific degree
measurement.
Suppose you want to rotate a shape by positive
\(90^\circ\).
You can use the notation
\(R_{90^\circ}\)
to identify this rotation.
Use mathematical notation to express a rotation of
positive
\(180^\circ\).
\(R_{180^\circ}\)
Level Up
The slideshow contained many new vocabulary terms related to the
rotation of objects in the coordinate plane. How well did you
understand them? Use the activity below to practice. Match the
term on the left with its definition on the right.
Great job!
Text
Guided Notes
Tutor
Video
How To
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