Unit: TransformationsStudent Handout 4

Name Answer Key

Date

ROTATIONS ON THE COORDINATE PLANE

A rotation turns a figure around a fixed point called the center of

rotationROTATIONS

• For our examples, the center of rotation will be the origin and we'll •

rotate in increments of

Pay attention to the direction of Consider each quadrant as another

the rotation! in the rotation.

DIRECTIONS AND 2700 *Starting point

DEGREES

1800clockwise counterclockwise

Find the number of degrees in each rotation shown below.

1.

clockwise

2700 counterclockwise

4.

2700 clockwise

POO counterclockwise

2. 3.

2700 1800clockwise clockwise

counterclockwise 1800 counterclockwise

5. 6.

1800 gooclockwise clockwise

1800 counterclockwise 2700 counterclockwise

17OManeuvering the Middle LLC, 20 '7

7. Rotate the figure shown at the right then 1800,and then 2700 clockwise. After each rotation, record

e coordinates of the image in the appropriate table,

Look for any patterns to try and create the algebraicrepresentation for each rotation.

*Before students have discovered any patterns, I havethem use a piece of patty paper to trace and create therotation on the graph. It's much easier for them tounderstand rotations when they can manipulate the figureand see it happen themselves.

CLOCKWISE

(270 0 COUNTERCLOCKWISE)

ALGEBRAIC REPRESENTATION:

IN YOUR WORDS:

-x and y values switched-x became opposite sign

180 0 CLOCKWISE

(1800 COUNTERCLOCKWISE)

ALGEBRAIC REPRESENTATION:

IN YOUR OWN WORDS:

-x and y values becameopposite signs

270 0 CLOCKWISE

(go o COUNTERCLOCKWISE)

A(ZI)

ALGEBRAIC REPRESENTATIN

IN YOUR OVNVORDS:

-x and y values switched-y became opposite sign

The coordinates below represent rotations. Use what you've learned today to describe what type of

rotation occurred.

90 0 clockwise or 270 0 counterclockwise

q. y 5) Y' -4) 270 0 clockwise or counterclockwise

180 0 clockwise or counterclockwise10. Z -l) + Z' (6, l)

*A helpful hint for students is to sketch a coordinate plane and note how many quadrants the point was

rotated. It's much easier to visualize it than to try and memorize the "rules".

12. Do rotations preserve or change the orientation11. Do rotations preserve or change the orientation

of the vertices Qof the figure Q Change

Summarize today's lesson:

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