Transformation

Transformation

​Rigid Motion

Rigid motion changes the location of an image, or the direction it is facing, but does not change the size or shape of it. The three basic rigid motions are translations, reflections, and rotations.

​Pre Image and Image

The new (transformed) shapes are called images and the original, unaltered shapes are called preimages.

Types of Transformation

​Transformation

• Reflection - Flips the pre-image and produces the mirror-image

• Rotation - Rotates or turns the pre-image around an axis

• Translation - Slides or moves the pre-image

• Dilation - Stretches or shrinks the pre-image

Reflections

• A reflection is a transformation that is a flip.

• A point or figure is reflected in a line called the line of reflection.

• A reflection is a mirror image of the preimage.

• Each point in the image and preimage is the same distance from the line of reflection.

• The image has the same shape and size as the preimage.

Reflect the image acros the x-axis and y-axis

See how the image is reflected in the example.

Multiple Choice

Is the picture being reflected in the y-axis or x-axis?

• y-axis
• x-axis

Multiple Choice

Where will A' be at, if triangle ABC is reflected by
(x,y) --> (-x,y)?

• (2,1)
• (1,-2)
• (-1,2)

Multiple Choice

If the dotted figure is the image, the original figure was reflected over the ...

• x-axis
• y-axis

The way to look at rotation is to look at a clock.

​Clockwise Rotation: is to the right

Counterclockwise is to the left​

Rotation​

​

Rotations

Multiple Choice

What type of rotation does this represent (from red to blue)?

• 270⁰ clockwise

• 180⁰

• 90⁰ clockwise

Multiple Choice

Rotation Rules (clockwise):

90^o rotation: (x, y)→(y, -x)

What are the coordinates for A' after a 90^⁰ rotation clockwise?

• (1, 3)

• (3, 1)

• (3, -1)

• (1, -3)

Multiple Choice

Rotate the point (-3,-4) around the origin 180 degrees. State the image of the point.

Rule: (x, y) ---- ( -x, -y)

• (-4, -3)

• (-4, 3)

• (4, -3)

• (3, 4)

Translations move

• to the left or to the right (horizontal) x

• up or down (vertical) y

Multiple Choice

Point M (-3, 5) is translated using this rule.

(x, y) ----> (x - 1, y)

What are the coordinates of M'?

• (-4, 5)

• (-2, 5)

• (-4, 4)

• (-3, 4)

Multiple Choice

Determine where Point T' would be if you translated Point T 6 units up and 3 units to the right.

• (5, 1)

• (5, 3)

• (6, 3)

• (3, 6)

Multiple Choice

Determine where X' would be if you translated X 3 units to the left and 9 units down.

• (-4, 4)
• (-10, 2)
• (-4, -5)
• (-1, 5)

​Dilation

Multiple Choice

A dilation is which of the following:

• only an enlargement

• only a reduction

• either an enlargement or a reduction

• neither an enlargement nor a reduction

Multiple Choice

State the coordinate of the image of the given point B (4,9) under a dilation with center at the origin with the given scale factor of 2.

• B' (2 , 4.5)

• B' (-8 ,-18)

• B' (8 ,18)

• B' (9 ,4)

Multiple Choice

What is the scale factor from the small fry to the large fry?

• 1/3

• 48

• 4

• 3

Summary