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 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.

Therefore, the English term that best represents reflection is "flip".

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.

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 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.

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.

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

"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"

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.