Transformational geometry

Transformational Geometry

Definitions of Transformations

Translation

The transformation of moving an object a certain distance.

The object stays the exact same, not having been reflected, rotated or re-sized.

Every point of the object moves in the same direction, and the same distance.

How to Perform a Translation (Directions)1. Pinpoint the X and Y location to translate

the object to.2. First, begin with the X axis, which is

horizontal on the Cartesian Graph. 3. Count a certain amount of spaces on the X

axis, and then mark the position.4. Next, continue with the Y axis, which is

vertical on the Cartesian Graph.5. Count a certain amount of spaces, and then

mark the position.6. Line up both markings and draw the shape

from the point it was translated.

How to Perform a Translation (Link)

(Click on Image)

Rotation

The transformation in which an object is turned around a fixed point. One point of the object is fixed.

The rest of the object pivots around the fixed point at any given angle.

1. Mark a point to rotate an object around.

2. Choose an angle, up to 359 o,

as well as clockwise, or counter clockwise.

3. Rotate the object at the previously chosen angle.

4. Redraw the object to the exact same size.

How to Perform a Rotation (Directions)

How to Perform a Rotation (Link)

(Click on Image)

The transformation in which a geometric figure is mirrored across a line Which creates a mirror image.

The line that mirrors the figure is called the axis of reflection.

Reflection

1. Pinpoint an axis of reflection.

2. Calculate how far away your object is from your axis of reflection.

3. Redraw your object the same distance away, but have it symmetrical.

How to Perform a Reflection (Directions)

How to Perform a Reflection (Link)

(Click on Image)

1. Translate a 2x1 unit rectangle by point D from -2, 4 to 3, -4.2. Reflect the rectangle across the axis of reflection provided.3. Rotate the rectangle clockwise 180o at point D

Transformation Question

D

BA

C

-1-2-3-4-5

-5 -4 -3 -2 -1

54321

1 2 3 4 5Axis of Reflection

D

BA

C

-1-2-3-4-5

-5 -4 -3 -2 -1

54321

1 2 3 4 5

Solution - Step One: Translation

D

BA

C

-1-2-3-4-5

-5 -4 -3 -2 -1

54321

1 2 3 4 5Axis of Reflection

Solution - Step Two: Reflection

-1-2-3-4-5

-5 -4 -3 -2 -1

54321

1 2 3 4 5Axis of Reflection

D

BA

C

-1-2-3-4-5

-5 -4 -3 -2 -1

54321

1 2 3 4 5Axis of Reflection

D

BA

C

Solution - Step Three: Rotation

-1-2-3-4-5

-5 -4 -3 -2 -1

54321

1 2 3 4 5Axis of Reflection

D

BA

C

-1-2-3-4-5

-5 -4 -3 -2 -1

54321

1 2 3 4 5Axis of Reflection

D BAC

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The End