<Math_Project>_<Quarter_4>_<Amari_Santana>_<5_5_2022>>

Object Transformations​

By Amari Santana

Notice the shape of the figure stays the same after a translation. All of the corresponding angles and sides are congruent, and all corresponding sides are parallel.

A translation is a transformation that "slides" a figure in any direction. It does not change the orientation or size of the figure.

​What is a Translation?​

Translations

Object Transformations

Multiple Choice

The translation to the left shows the pentagon undergoing which transformation?

• A reflection across the X-axis

• A 90 degree rotation from the origin

• A translation 11.25 units to the East

• A translation 5 units right

Notice the shape of the figure stays the same after a reflection. All of the corresponding angles and sides are congruent. Notice the shape of the figure stays the same after a reflection. All of the corresponding angles and sides are congruent.

A reflection is a transformation in which the figure flips over a line of reflection. The objects are mirror images of each other.

​

​What is a Reflection?​

Reflections

Object Transformations

Multiple Choice

The graph shows a reflection across which axis?

• X - axis

• Y - axis

• Z - axis

• The example shown is not a reflection

Notice the shape of the figure stays the same after a reflection. All of the corresponding angles and sides are congruent. Notice the shape of the figure stays the same after a reflection. All of the corresponding angles and sides are congruent.

A rotation is a transformation in which a figure is rotated on the coordinate grid, it turns or pivots about a point. The shape of the figure stays the same after a rotation. All of the corresponding angles and sides are congruent.

​What is a Rotation?​

Rotations

Object Transformations

Multiple Choice

The following shows a rotation about the origin, of __________.

• 45 degrees

• 90 degrees

• 180 degrees

• 360 degrees

Rotation Rules are used to find the location of a​ point on a grid after a rotation. The table to the right is a list of the rotation rules for clockwise and counter-clockwise rotations.

​What are Rotation Rules?​

Rotation Rules

Object Transformations

Counter-Clockwise​	​Rules	Clockwise​
90​°	(-y,x)	​270°​
180​°​	(-x,-y)​	180​​°
270​​°	(y,-x)​	90​​°
360​​°	​(x,y)	360​°

​Notice that A rotation of 180° (clockwise and counterclockwise) of a vertex about a point will result in the image with the same distances from the point of rotation in the horizontal and vertical directions, but in opposite directions. A 270° counterclockwise rotation is the same as a 90° clockwise rotation. A 270° clockwise rotation is the same as a 90° counterclockwise rotation.

Multiple Choice

What would be the new coordinates of point X if the figure below was rotated 270° clockwise about the point (1, -2)?

• (-2,2)

• (-3,5)

• (-1, 2)

• (2, -2)

Multiple Select

What should we with the Panda?

• Turn him into a Dog Toy

• Take out his Stuffing, and fill it with Cotton Candy

• Dye him Pink

• Hug him

  Till' he Farts

Notice the shape of the figure stays the same after a reflection. All of the corresponding angles and sides are congruent. Notice the shape of the figure stays the same after a reflection. All of the corresponding angles and sides are congruent.

A dilation is a transformation which produces an image that is the same shape as the original, but is a different size. The original figure and the dilated image are similar figures, which means the angles are congruent and the side lengths are proportional.

​What is a Dilation?​

Dilations

Object Transformations

Multiple Choice

Triangle ABC is dilated to create triangle XYZ. What are the coordinates of Z?

• (0,-1)

• (-1,0)

• (-2,0)

• (0,-2)

Notice that the new side lengths of the dilated triangle can be found by multiplying the original side lengths by a scale factor of 2.

Scale factor is the ratio of the side length of the dilated image to the side length of the original figure.

​What is a Scale Factor?​

Scale Factor

Object Transformations

Multiple Choice

Which of the following is the correct Scale Factor from triangle DEF to triangle D'E'F'?

• 0.25

• 0.5

• 4

• 4.25

Open Ended

The Rectangle KLMN is dilated from point (-5,5) to create rectangle PTRN. What are the coordinates of vertex T? Explain.

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