Common Core: 8th Grade Math : Grade 8

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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Example Questions

Example Question #8 : Describe The Effect Of Dilations, Translations, Rotations, And Reflections: Ccss.Math.Content.8.G.A.3

What is the scale of the dilation that the blue rectangle underwent to get the purple rectangle in the image provided? 


15

Possible Answers:

Correct answer:

Explanation:

A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor. Let's look at the image in the picture and determine the length and width of each of the rectangles:

16

Notice that both the length and the width of the rectangle quadruples  in the purple rectangle, from the blue rectangle; thus the scale of the dilation is 

Example Question #9 : Describe The Effect Of Dilations, Translations, Rotations, And Reflections: Ccss.Math.Content.8.G.A.3

What is the scale of the dilation that the blue rectangle underwent to get the purple rectangle in the image provided? 


17

Possible Answers:

Correct answer:

Explanation:

A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor. Let's look at the image in the picture and determine the length and width of each of the rectangles:

18

Notice that both the length and the width of the rectangle is five times the size in the purple rectangle, from the blue rectangle; thus the scale of the dilation is 

Example Question #10 : Describe The Effect Of Dilations, Translations, Rotations, And Reflections: Ccss.Math.Content.8.G.A.3

What is the scale of the dilation that the blue rectangle underwent to get the purple rectangle in the image provided? 


19

Possible Answers:

Correct answer:

Explanation:

A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor. Let's look at the image in the picture and determine the length and width of each of the rectangles:

20

Notice that both the length and the width of the rectangle triples in the purple rectangle, from the blue rectangle; thus the scale of the dilation is 

Example Question #371 : Grade 8

What is the scale of the dilation that the blue rectangle underwent to get the purple rectangle in the image provided? 


21

Possible Answers:

Correct answer:

Explanation:

A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor. Let's look at the image in the picture and determine the length and width of each of the rectangles:

22

Notice that both the length and the width of the rectangle is a fourth of the size in the purple rectangle, from the blue rectangle; thus the scale of the dilation is 

Example Question #52 : Geometry

What is the scale of the dilation that the blue rectangle underwent to get the purple rectangle in the image provided? 


23

Possible Answers:

Correct answer:

Explanation:

A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor. Let's look at the image in the picture and determine the length and width of each of the rectangles:

24

Notice that both the length and the width of the rectangle are a third of the size in the purple rectangle, from the blue rectangle; thus the scale of the dilation is 

Example Question #1 : Understand Similarity Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.4

Are the two dimensional shapes shown on the coordinate plane provided similar? If yes, do the shapes show a transformation or a dilation? 


2

Possible Answers:

Yes, dilation 

Yes, both transformation and dilation 

Yes, transformation 

No

Correct answer:

Yes, transformation 

Explanation:

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

  • Rotation: A rotation means turning an image, shape, line, etc. around a central point.
  • Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
  • Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The two shapes provided are both pentagons and they are the same size; thus, the shapes are similar and they have gone through a transformation. 

Example Question #2 : Understand Similarity Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.4

Are the two dimensional shapes shown on the coordinate plane provided similar? If yes, do the shapes show a transformation or a dilation? 

1

Possible Answers:

Yes, transformation

No

Yes, dilation 

Yes, both transformation and dilation 

Correct answer:

Yes, transformation

Explanation:

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

  • Rotation: A rotation means turning an image, shape, line, etc. around a central point.
  • Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
  • Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The two shapes provided are both pentagons and they are the same size; thus, the shapes are similar and they have gone through a transformation. 

Example Question #62 : Geometry

Are the two dimensional shapes shown on the coordinate plane provided similar? If yes, do the shapes show a transformation or a dilation? 

3

Possible Answers:

Yes, dilation 

No

Yes, transformation

Yes, both a transformation and dilation 

Correct answer:

Yes, transformation

Explanation:

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

  • Rotation: A rotation means turning an image, shape, line, etc. around a central point.
  • Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
  • Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The two shapes provided are both pentagons and they are the same size; thus, the shapes are similar and they have gone through a transformation. 

 

Example Question #4 : Understand Similarity Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.4

Are the two dimensional shapes shown on the coordinate plane provided similar? If yes, do the shapes show a transformation or a dilation? 


4

Possible Answers:

Yes, transformation

Yes, dilation 

Yes, both a transformation and dilation 

No

Correct answer:

Yes, transformation

Explanation:

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

  • Rotation: A rotation means turning an image, shape, line, etc. around a central point.
  • Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
  • Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The two shapes provided are both pentagons and they are the same size; thus, the shapes are similar and they have gone through a transformation. 

 

Example Question #3 : Understand Similarity Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.4

Are the two dimensional shapes shown on the coordinate plane provided similar? If yes, do the shapes show a transformation or a dilation? 


5

Possible Answers:

No

Yes, both a transformation and dilation 

Yes, dilation 

Yes, transformation

Correct answer:

Yes, both a transformation and dilation 

Explanation:

In order for two shapes to be similar, they must be the same shape. If the shapes are the same, but are a different size or facing a different direction, then the shapes can still be similar if and only if they have gone through a dilation or a transformation. 

Let's recall our key terms:

Dilation: A dilation creates an image of the same shape, but of a different size. Dilations are always done with a certain scale factor, and the scale factor must be equal for all sides of the shape. 

Transformation: A transformation can be described in three ways:

  • Rotation: A rotation means turning an image, shape, line, etc. around a central point.
  • Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.
  • Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

The yellow rectangle is smaller than the blue rectangle. In fact, both the length and the width are half the size; thus, the shape has gone through a dilation. The yellow rectangle is also in a different position; thus, the shape has gone through a transformation.  

 

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