Represent and Compare Transformations in the Plane: CCSS.Math.Content.HSG-CO.A.2 - Common Core: High School - Geometry
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A basketball player is able to perfectly spin a basketball on his index finger. While the basketball is spinning, what mathematical expression can be concluded about it?
A basketball player is able to perfectly spin a basketball on his index finger. While the basketball is spinning, what mathematical expression can be concluded about it?
This question is applying mathematical and more specifically, geometric definitions to describe a real life situation. Geometric definitions usually correspond to objects in the 2 dimensional plane or 3 dimensional surface. Since the basket ball is the object in question, this problem is dealing with a the 3 dimensional space.
From here, recall what is given
"A basketball player is able to perfectly spin a basketball on his index finger."
The index finger in this particular situation is acting as an axis for the basketball. Since the basketball is spinning and is maintaining its shape and size, this is considered a "rotation" in geometry.
Therefore, the correct answer is
"The basketball is in rotation"
This question is applying mathematical and more specifically, geometric definitions to describe a real life situation. Geometric definitions usually correspond to objects in the 2 dimensional plane or 3 dimensional surface. Since the basket ball is the object in question, this problem is dealing with a the 3 dimensional space.
From here, recall what is given
"A basketball player is able to perfectly spin a basketball on his index finger."
The index finger in this particular situation is acting as an axis for the basketball. Since the basketball is spinning and is maintaining its shape and size, this is considered a "rotation" in geometry.
Therefore, the correct answer is
"The basketball is in rotation"
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A trolley car is attached to metal ground rails that go from the most southern block in a city to the most northern block of that same city. If the trolley starts at the south end and moves all the way to the northern end, what type of geometric expression does this situation define?
A trolley car is attached to metal ground rails that go from the most southern block in a city to the most northern block of that same city. If the trolley starts at the south end and moves all the way to the northern end, what type of geometric expression does this situation define?
To answer this question first recall the different geometric definitions that correspond to the listed possible answer choices.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Looking at the given situation,
"A trolley car is attached to metal ground rails that go from the most southern block in a city to the most northern block of that same city. If the trolley starts at the south end and moves all the way to the northern end, what type of geometric expression does this situation define?"
it can be seen that the trolley is not changing shape, it is not rotating nor reflecting. It is however, moving a certain distance from its starting position thus the definition of a translation and a transformation.
To answer this question first recall the different geometric definitions that correspond to the listed possible answer choices.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Looking at the given situation,
"A trolley car is attached to metal ground rails that go from the most southern block in a city to the most northern block of that same city. If the trolley starts at the south end and moves all the way to the northern end, what type of geometric expression does this situation define?"
it can be seen that the trolley is not changing shape, it is not rotating nor reflecting. It is however, moving a certain distance from its starting position thus the definition of a translation and a transformation.
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State the transformation of the red rectangle to the black rectangle.
State the transformation of the red rectangle to the black rectangle.
To answer this question first recall the different geometric definitions that correspond to the listed possible answer choices.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Now, examine the given image and choose the appropriate answer.
Looking at the red rectangle it is seen that the coordinate points of the vertices are:
The coordinate points of the vertices for the black triangle are:
Therefore, the red rectangle is being reflected over the 
axis or it is being slide up four units. Thus, the correct answer is both a reflection and a translation.
To answer this question first recall the different geometric definitions that correspond to the listed possible answer choices.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Now, examine the given image and choose the appropriate answer.
Looking at the red rectangle it is seen that the coordinate points of the vertices are:
The coordinate points of the vertices for the black triangle are:
Therefore, the red rectangle is being reflected over the
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Mrs. Johnson's classroom is organized in a grid pattern. In her classroom there are 
rows and 
columns of desks resulting in a total of 
desks. Which of the following depicts the resulting mathematical function of the situation, given Billy sits in desk 
and wants to move 
desks to the south and 
desk to the east.
Assume south represents a negative directional change in the 
axis and east represents a positive directional change in the 
axis.
Mrs. Johnson's classroom is organized in a grid pattern. In her classroom there are 
Assume south represents a negative directional change in the
To help solve this problem, look at the desks as a coordinate grid. Given that Billy currently sits in desk 
and assuming south represents a negative directional change in the 
axis and east represents a positive directional change in the 
axis, we can write the following transformation.
Since Billy wants to move 2 desks south or in the "down" direction then the mathematical notation would be,
Now since Billy also wants to move one desk to the east this results in the following,
From here, plug in the starting position which is 
and formulate the final transformation.
To help solve this problem, look at the desks as a coordinate grid. Given that Billy currently sits in desk
Since Billy wants to move 2 desks south or in the "down" direction then the mathematical notation would be,
Now since Billy also wants to move one desk to the east this results in the following,
From here, plug in the starting position which is
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Which one of the following best describes a reflection?
Which one of the following best describes a reflection?
To answer this question first recall the different geometric definitions.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Therefore, the English term that best represents reflection is "flip".
To answer this question first recall the different geometric definitions.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Therefore, the English term that best represents reflection is "flip".
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Which one of the following best describes a translation?
Which one of the following best describes a translation?
To answer this question first recall the different geometric definitions.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Therefore, the English term that best represents translation is "slide".
To answer this question first recall the different geometric definitions.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Therefore, the English term that best represents translation is "slide".
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Dilation is a type of __________.
Dilation is a type of __________.
To answer this question first recall the different geometric definitions.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Since dilation is when an object changes size, that means dilation is a type of transformation.
To answer this question first recall the different geometric definitions.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Since dilation is when an object changes size, that means dilation is a type of transformation.
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Which one of the following best describes a rotation?
Which one of the following best describes a rotation?
To answer this question first recall the different geometric definitions.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate or turn an object either clockwise or counter clockwise around a center point.
Therefore, the English term that best represents rotation is "turn".
To answer this question first recall the different geometric definitions.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate or turn an object either clockwise or counter clockwise around a center point.
Therefore, the English term that best represents rotation is "turn".
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Billy is flying a kite at the park. The kite starts touching the spool of string it is attached to. As Billy runs, the spool of string unravels and the kite flies 
feet in the air. Which geometric term describes this situation?
Billy is flying a kite at the park. The kite starts touching the spool of string it is attached to. As Billy runs, the spool of string unravels and the kite flies 
This question is applying mathematical and more specifically, geometric definitions to describe a real life situation. Geometric definitions usually correspond to objects in the 2 dimensional plane or 3 dimensional surface. Since the basket ball is the object in question, this problem is dealing with a the 3 dimensional space.
From here, recall what is given
"Billy is flying a kite at the park. The kite starts touching the spool of string it is attached to. As Billy runs, the spool of string unravels and the kite flies 20 feet in the air."
Recall that a translation is to move an object from its original position a certain distance without changing the object in any other way. Since the kit does not change size of shape but it does move a certain distance from where it originally started, this matches a translation.
Therefore, the correct answer is
"Translation"
This question is applying mathematical and more specifically, geometric definitions to describe a real life situation. Geometric definitions usually correspond to objects in the 2 dimensional plane or 3 dimensional surface. Since the basket ball is the object in question, this problem is dealing with a the 3 dimensional space.
From here, recall what is given
"Billy is flying a kite at the park. The kite starts touching the spool of string it is attached to. As Billy runs, the spool of string unravels and the kite flies 20 feet in the air."
Recall that a translation is to move an object from its original position a certain distance without changing the object in any other way. Since the kit does not change size of shape but it does move a certain distance from where it originally started, this matches a translation.
Therefore, the correct answer is
"Translation"
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Which of the following describes the change in the red polygon to the black polygon?
Which of the following describes the change in the red polygon to the black polygon?
To answer this question first recall the different geometric definitions that correspond to the listed possible answer choices.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Now, examine the given image and choose the appropriate answer.
First, it is clear to see that the black polygon is larger than the red polygon. Therefore, a transformation has occurred since the original image has been resized. Also, the black polygon is in quadrant one while the red polygon is in quadrant three, therefore a slide or translation has occurred.
Thus the correct answer is,
"Transformation and Translation"
To answer this question first recall the different geometric definitions that correspond to the listed possible answer choices.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Now, examine the given image and choose the appropriate answer.
First, it is clear to see that the black polygon is larger than the red polygon. Therefore, a transformation has occurred since the original image has been resized. Also, the black polygon is in quadrant one while the red polygon is in quadrant three, therefore a slide or translation has occurred.
Thus the correct answer is,
"Transformation and Translation"
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Which of the following describes the change in the red circle to the black circle?
Assume the center of the circles are the same.
Which of the following describes the change in the red circle to the black circle?
Assume the center of the circles are the same.
To answer this question first recall the different geometric definitions that correspond to the listed possible answer choices.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Now, examine the given image and choose the appropriate answer.
First, it is clear to see that the black circle is smaller than the red circle. Therefore, a transformation has occurred since the original image has been resized. Since it is stated that the centers of the circles are the same it can be concluded that only a resizing has occurred.
Thus the correct answer is,
"Transformation"
To answer this question first recall the different geometric definitions that correspond to the listed possible answer choices.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Now, examine the given image and choose the appropriate answer.
First, it is clear to see that the black circle is smaller than the red circle. Therefore, a transformation has occurred since the original image has been resized. Since it is stated that the centers of the circles are the same it can be concluded that only a resizing has occurred.
Thus the correct answer is,
"Transformation"
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Determine whether the statement is true or false:
When a person's palm is faced down on a desk and that person then flips their hand over, their palm can be described as a reflection.
Determine whether the statement is true or false:
When a person's palm is faced down on a desk and that person then flips their hand over, their palm can be described as a reflection.
To answer this question first recall the different geometric definitions that correspond to the listed possible answer choices.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Now look at the specific event in this problem.
"When a person's palm is faced down on a desk and that person then flips their hand over, their palm can be described as a reflection."
Even though reflection is known as the "flipping" of an object it does not describe this situation because the palm of someones hand has different characteristics than the top of the hand therefore, the statement in this particular problem in false.
To answer this question first recall the different geometric definitions that correspond to the listed possible answer choices.
Translation: To move an object from its original position a certain distance without changing the object in any other way.
Transformation: Refers to any of the four changes that can be done to an object geographically. Transformations include, reflections, translations, rotations, and resizing the object.
Reflection: To flip the orientation of an object over a specific line or function.
Rotation: To rotate an object either clockwise or counter clockwise around a center point.
Now look at the specific event in this problem.
"When a person's palm is faced down on a desk and that person then flips their hand over, their palm can be described as a reflection."
Even though reflection is known as the "flipping" of an object it does not describe this situation because the palm of someones hand has different characteristics than the top of the hand therefore, the statement in this particular problem in false.
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