TRANSFORMATIONS

EXPORT AND IMPORT INDUSTRY

EXPORT AND IMPORTS

EXPORTS AND IMPORTS

EXPORTS AND IMPORTS

TRANSFORMATIONS

• A transformation is an operation on a geometric figure

that preserves a one-to-one correspondence between

every point in the original figure and a new point on the

transformed image of the figure.

• In friendlier terms, a transformation is simply a

movement or change from an original image (preimage)

within a coordinate plane to a new location.

PRIME NOTATION

• The preimage is the original location of a point or figure.

• The image occurs after a transformation takes place, and is

signified with an accent mark beside the new point (Prime

Notation)

Example:

THE FOUR TYPES OF

TRANSFORMATIONS

• Translation: Creates a new image of a geometric figure by

sliding it to the left, right, up or down to a new location.

• Example:

TRANSLATION

• When translating (sliding) a figure on a coordinate plane the figure can

move vertically (up or down), horizontally (left or right), or a

combination of the two.

• Let’s watch a transformation in action!

• It is important to remember that a translation DOES NOT change the

size or orientation of the figure, simply its location

• http://www.virtualnerd.com/middle-math/integers-coordinate-plane/transformations/translation-

definition

TRANSLATION

Let’s try a few!

1. If point A is at -4, 1 and translates 7

units to the right, which quadrant will

A’ be located?

2. If point A moved 3 units down,

which quadrant will A’ be located?

3. If A’ is located at (2, -6), what

translation took place? (It looks tricky,

but I PROMISE you it’s not!)

4. B’ is located at (3, 6). The translation

that took place was (x - 2, y + 10). In

which quadrant is the preimage

located?

THE FOUR TYPES OF

TRANSFORMATIONS

• Reflection: Creates a mirror image of a geometric figure when each point is

the same distance from the line of reflection.

• Examples:

REFLECTION

• A reflection occurs when your image is flipped across a line of reflection.

• To create an exact replica, the preimage and corresponding image points must be equal distance from the line of reflection.

• It is important to remember that a reflection DOES NOT change the size of the figure, simply its orientation and location

• https://www.youtube.com/watch?v=j1X_UIOvEwA

REFLECTION

Let’s try a few!

Plot the preimage N(-4, 1), O(-2, 6), P(-1, 2).

1. If reflected across the x-axis, in which

quadrant will the image be located?

a. What are the coordinates of the

image created by the transformation?

2. If the preimage is reflected across the

y-axis, in which quadrant will the image

be located?

a. What are the coordinates of the

image created by the transformation?

THE FOUR TYPES OF

TRANSFORMATIONS

• Rotation: Create a new image of a

geometric figure by rotating (turning) it

clockwise or counter-clockwise

• For the purposes 8th grade content, we

will focus on rotations of 90o increments

the origin of the coordinate graph

ROTATION

• The origin is the point where the x and y-axis intersect.

• Clockwise rotates the figure around the coordinate plane in a rightward motion

• Counter-clockwise rotates the figure around the coordinate plane in a leftward motion

ROTATION

• It is important to remember that a rotation DOES NOT change

the size of the figure, simply its orientation and location

ROTATION

Let’s try a few!

Plot the preimage N(-4, 1), O(-2, 6), P(-1, 2).

1. If rotated 270o clockwise, in which

quadrant will the image be located?

a. What are the coordinates of the

image created by the transformation?

2. If the preimage is rotated 180o, in

which quadrant will the image be

located?

a. What are the coordinates of the

image created by the transformation?

THE FOUR TYPES OF

TRANSFORMATIONS

• Dilation: Create a larger or smaller image of a geometric figure.

• The amount of increase or decrease in the size of the geometric figure is

called the scale factor. All points of the preimage are multiplied by the

scale factor to determine the new coordinates of the image.

DILATION

• The figure will get larger when

the scale factor is greater than 1

• The figure will get smaller when

the scale factor is less than 1

• It is important to remember that a

dilation DOES NOT change the

orientation of the figure, simply its

size and location

DILATION

• How do you determine the new coordinates when given the scale factor?

• Simply multiply each coordinate by the value to get the new coordinates.

• If you given the coordinates for a figure: (2, 5), (1,2 ), (8, 4) and the scale factor is 2, then multiply each x and y value by 2 to get your new set of coordinates-(4, 10), (2, 4), (16, 8)

• IT’S THAT EASY!!!

• https://www.youtube.com/watch?v=K2HT4eTW0vc

• Accelerated: https://www.youtube.com/watch?v=4Yap2t_v034

The preimage N(-4, 2), O(-2, 6), P(-2, 2).

1. If the scale factor is 1.5 what will happen to the figure?

2. If the scale factor is ¾ what will happen to the figure?

3. If the preimage is dilated by a scale factor of 3, what are the

coordinates of the new image?

4. If the preimage is dilated by a scale factor of ½, what are the

coordinates of the new image?