6th Grade Math Textbook, Fundamentals

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13-11

270° counterclockwise

around the origin

So A(3, 0) A(0, 3)

B(5, 2) B(2, 5)

C(0, 1) C(1, 0)

Graph Rotations

Objective To demonstrate rotation of points on a coordinate plane in clockwise and

counterclockwise directions• To identify graphs of rotations of figures• To graph rotations of

polygons on a coordinate plane

Jaime is creating a design from a triangle. He creates one design
rotating the figure around the origin 270 counterclockwise.
He creates another design rotating the figure around the
origin 90 counterclockwise and yet another rotating the
figure around the origin 180 counterclockwise. What are
the coordinates for each image of the triangle?

A is a transformation that turns a figure around a

point, usually in a counterclockwise direction. The point

around which the figure rotates is called the.

As with reflections and translations, the image of a rotation

is congruent to the original figure.

A 90 rotation is a quarter turn.

A 180 rotation is a half turn.

A 270 rotation is a three-quarter turn.

center of rotation

rotation

0

y

x

  























A

A‘

B‘

C‘

ƒ

B

C

0

y

x

  























A

B

C

0

y

x

  























A

A‘

ƒ

C‘

B‘

B

C

90° counterclockwise

around the origin

So A(3, 0) A(0, 3)

B(5, 2) B(2, 5)

C(0, 1) C(1, 0)

Think

Counterclockwise refers to the

direction opposite to the way

the hands on a clock rotate.

180° counterclockwise

around the origin

So A(3, 0) A(3, 0)

B(5, 2) B(5, 2)

C(0, 1) C(0, 1)

0

y

x

 























A‘ A

C‘

B‘

B

C

ƒ