Common Core: High School - Geometry : Rotations and Reflections of Rectangles, Parallelograms, Trapezoids, and Regular Polygons: CCSS.Math.Content.HSG-CO.A.3

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Example Questions

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Example Question #1 : Rotations And Reflections Of Rectangles, Parallelograms, Trapezoids, And Regular Polygons: Ccss.Math.Content.Hsg Co.A.3

Determine whether the statement is true or false:

The following image can be divided multiple ways to result in a reflected image.

Screen shot 2016 06 14 at 7.55.09 am

Possible Answers:

False

True

Correct answer:

False

Explanation:

Looking at the statement and the image given, it is seen that the object is a trapezoid.

A trapezoid has two bases of differing lengths and two side pieces of equal length in this particular case.

Screen shot 2016 06 14 at 7.55.09 am

For an object to be divided into images that can be reflected onto one another, the images must be identically mirrored.

To identify the possible solutions, draw the lines of symmetry.

Screen shot 2016 06 14 at 7.55.09 am

Only one line of symmetry could be drawn to allow for two images of the trapezoid to be reflected over that line. The trapezoid cannot be divided in any other way that will result in a reflected image.

Therefore, the original statement is false.

Example Question #2 : Rotations And Reflections Of Rectangles, Parallelograms, Trapezoids, And Regular Polygons: Ccss.Math.Content.Hsg Co.A.3

Given a hexagon, how many lines of symmetry exist?

Possible Answers:

Twelve

Two

Six

Four

Three

Correct answer:

Six

Explanation:

Recall that a hexagon is a six sided figure. Now recall that a line of symmetry creates two mirrored, identical figures which is also known as a reflection.

Knowing these two pieces of information draw the image of the hexagon and the lines of symmetry

Hexagon

Counting up these lines results 6 lines of symmetry.

Therefore, the answer is 6.

Example Question #3 : Rotations And Reflections Of Rectangles, Parallelograms, Trapezoids, And Regular Polygons: Ccss.Math.Content.Hsg Co.A.3

A cylinder is composed of two circular bases. For one base to be carried onto the other, what geometric transformation must occur?

Possible Answers:

Extension

Translation

Rotation and Translation

Rotation

All of the answers are correct.

Correct answer:

Translation

Explanation:

Since a cylinder is composed of two, identical circular bases that are separated by the height of the cylinder, the transformation that must occur to have one carried onto the other is a translation. Recall that a translation is the sliding of an object without changing its size or shape. Therefore, for the one base to be carried onto the other, translation is the geometric transformation that must occur.

Example Question #4 : Rotations And Reflections Of Rectangles, Parallelograms, Trapezoids, And Regular Polygons: Ccss.Math.Content.Hsg Co.A.3

If the rectangle is reflected across the x-axis, what is the resulting image?

Rotation

Possible Answers:

None of the other answers.

Rotation3

Rotation3

Rotation3

Rotation

Correct answer:

Rotation3

Explanation:

In order to create the resulting image of a reflection first recall what a reflection is.

Reflection: To flip the orientation of an object over a specific line or function.

In this specific situation the line of reflection is the x-axis.

The original image is,

Rotation

When the image is reflected across the x-axis result in,
Rotation3

This is the correct answer.

Example Question #5 : Rotations And Reflections Of Rectangles, Parallelograms, Trapezoids, And Regular Polygons: Ccss.Math.Content.Hsg Co.A.3

Given a trapezoidal based prism how can one base be carried onto the other?

Possible Answers:

None of the answers.

Translation

Extension

Rotation

Reflection

Correct answer:

Translation

Explanation:

Since a trapezoidal based prism is composed of two, identical trapezoidal bases that are separated by the height of the prism, the transformation that must occur to have one base carried onto the other is a translation. Recall that a translation is the sliding of an object without changing its size or shape. Therefore, for the one base to be carried onto the other, translation is the geometric transformation that must occur.

Example Question #6 : Rotations And Reflections Of Rectangles, Parallelograms, Trapezoids, And Regular Polygons: Ccss.Math.Content.Hsg Co.A.3

Determine whether the statement is true or false:

Reflections and rotations never result in the same image.

Possible Answers:

True

False

Correct answer:

False

Explanation:

To determine whether the statement is true or false, identify any example that would make the statement false.

"Reflections and rotations never result in the same image."

Imagine a square that exists in quadrant two. When this image is reflected across the y-axis it is still a square that is now in quadrant one. When the square from quadrant two is rotated around the origin, it results in the same image in quadrant one. Therefore, it is possible for a reflection and rotation to result in the same image.

Thus, the statement "Reflections and rotations never result in the same image." is false.

Example Question #7 : Rotations And Reflections Of Rectangles, Parallelograms, Trapezoids, And Regular Polygons: Ccss.Math.Content.Hsg Co.A.3

If the rectangle is rotated clockwise around the origin  degrees, what is the resulting image?

Rotation

Possible Answers:

Rotation3

Rotation3

Rotation

Rotation3

None of the answers.

Correct answer:

Rotation3

Explanation:

To rotate the rectangular object around the origin, first recall the definition for a rotation and origin.

Rotation: To rotate an object either clockwise or counter clockwise around a center point. In this particular case the center point is the origin or the point  where the x and y axis intersect.

Looking at the original image and making one 90 degree rotation around the origin results in the following.

Rotation

Rotation1

When rotating, the bottom right point will become the bottom left point, the top right point becomes the bottom right point, the left bottom point becomes the top left point, and the left top point becomes the top right point. 

Now, rotating it another  degrees to get to the  degree rotated image, results in the following

Rotation3

Example Question #8 : Rotations And Reflections Of Rectangles, Parallelograms, Trapezoids, And Regular Polygons: Ccss.Math.Content.Hsg Co.A.3

If the rectangle is rotated clockwise around the origin  degrees, what is the resulting image?

Rotation

Possible Answers:

Rotation3

Rotation

Rotation3

Rotation3

None of the answers.

Correct answer:

Rotation3

Explanation:

To rotate the rectangular object around the origin, first recall the definition for a rotation and origin.

Rotation: To rotate an object either clockwise or counter clockwise around a center point. In this particular case the center point is the origin or the point  where the x and y axis intersect.

Looking at the original image and making one rotation around the origin results in the following.

Rotation

Rotation1

When rotating, the bottom right point will become the bottom left point, the top right point becomes the bottom right point, the left bottom point becomes the top left point, and the left top point becomes the top right point. The visual representation for this rotation is as follows.

Rotation3

Example Question #9 : Rotations And Reflections Of Rectangles, Parallelograms, Trapezoids, And Regular Polygons: Ccss.Math.Content.Hsg Co.A.3

If the rectangle is rotated clockwise around the origin  degrees, what is the resulting image?

Rotation

Possible Answers:

Rotation


Rotation3

Rotation3

Rotation3

Rotation3

Correct answer:


Rotation3

Explanation:

To rotate the rectangular object around the origin, first recall the definition for a rotation and origin.

Rotation: To rotate an object either clockwise or counter clockwise around a center point. In this particular case the center point is the origin or the point  where the x and y axis intersect.

Looking at the original image and making one  degree rotation around the origin results in the following.

Rotation

Rotation1

When rotating, the bottom right point will become the bottom left point, the top right point becomes the bottom right point, the left bottom point becomes the top left point, and the left top point becomes the top right point. 

Now, rotating it another  degrees to get to the  degree rotated image, results in the following

Rotation3

From here one final rotation must occur to reach  degrees.

Rotation3

Example Question #10 : Rotations And Reflections Of Rectangles, Parallelograms, Trapezoids, And Regular Polygons: Ccss.Math.Content.Hsg Co.A.3

If the rectangle is rotated clockwise around the origin  degrees, what is the resulting image?

Rotation

Possible Answers:

Rotation3

Rotation3

Rotation

Rotation3

Rotation3

Correct answer:

Rotation

Explanation:

To rotate the rectangular object around the origin, first recall the definition for a rotation and origin.

Rotation: To rotate an object either clockwise or counter clockwise around a center point. In this particular case the center point is the origin or the point  where the x and y axis intersect.

Looking at the original image and making one 90 degree rotation around the origin results in the following.

Rotation

Rotation1

When rotating, the bottom right point will become the bottom left point, the top right point becomes the bottom right point, the left bottom point becomes the top left point, and the left top point becomes the top right point. 

Now, rotating it another  degrees to get to the  degree rotated image, results in the following

Rotation3

From here another rotation must occur to reach  degrees.

Rotation3

Lastly, complete one more  degree rotation to land at the  degree mark. Notice that rotating 360 degrees lands the image back at its original spot.

Rotation

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All Common Core: High School - Geometry Resources

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