Common Core: High School - Geometry : Congruence

Study concepts, example questions & explanations for Common Core: High School - Geometry

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All Common Core: High School - Geometry Resources

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Example Questions

Example Question #3 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , , , and  and after a transformation results in the coordinates , , , and  identify the transformation.

Possible Answers:

Reflection

None of the other answers.

Rotation

Dilation

Extension

Correct answer:

Reflection

Explanation:

"If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation."

A transformation that changes the  values by multiplying them by negative one is known as a reflection across the -axis or the line  

Therefore, this particular rectangle is being reflected across the -axis because the opposite of all the  values have been taken.

Example Question #4 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

If a rectangle has the coordinate values, , and  and after a transformation results in the coordinates , and  identify the transformation.

Possible Answers:

Rotation

Dilation

Translation

Reflection

None of the other answers.

Correct answer:

Translation

Explanation:

To identify the transformation that is occurring in this particular problem, recall the different transformations.

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 starting and ending coordinates of the rectangle,

 , and   to  , and 

Since all the  coordinates are increasing by two this is known as a translation.

Example Question #5 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the horizontal axis on the coordinate grid and is equivalent to the line .

Plot the points of the original trapezoid on the coordinate grid.

Screen shot 2016 06 15 at 5.49.55 am

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,

Screen shot 2016 06 15 at 5.51.13 am

Therefore, the coordinates of the reflected trapezoid are

Example Question #6 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the vertical axis on the coordinate grid and is equivalent to the line .

Plot the points of the original trapezoid on the coordinate grid.

Screen shot 2016 06 15 at 5.49.55 am

From here, to reflect the image across the -axis take the opposite of all the  values.

This change results in the following,

Screen shot 2016 06 15 at 6.02.01 am

Therefore, the coordinates of the reflected trapezoid are

Example Question #7 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , , and . What are the coordinates of this trapezoid after it is reflected across the  and -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the trapezoid, first identify how it is being reflected. This particular problem states that it is being reflected over the  and -axis. This means the reflected image will be in the fourth quadrant.

Plot the points of the original trapezoid on the coordinate grid.

Screen shot 2016 06 15 at 5.49.55 am

From here, to reflect the image across the line both axis take the opposite of all the coordinate values.

This change results in the following,

Screen shot 2016 06 15 at 6.19.15 am

Therefore, the coordinates of the reflected trapezoid are

Example Question #1 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , and . What are the coordinates of this trapezoid after it is reflected across the -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the vertical axis on the coordinate grid and is equivalent to the line .

Plot the points of the original triangle on the coordinate grid.

Screen shot 2016 06 15 at 6.33.25 am

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,


Screen shot 2016 06 15 at 6.52.29 am

Therefore, the reflected triangle has coordinates at

Example Question #9 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a trapezoid are, , , and . What are the coordinates of this triangle after it is reflected across the  and -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the  and -axis. This means the reflected image will be in the fourth quadrant.

Plot the points of the original trapezoid on the coordinate grid.

Screen shot 2016 06 15 at 6.33.25 am

From here, to reflect the image across the line both axis take the opposite of all the coordinate values.

This change results in the following,

Screen shot 2016 06 15 at 7.35.06 am

Therefore, the coordinates of the reflected triangle are

Example Question #1 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

The coordinates of a triangle are, , , and . What are the coordinates of this triangle after it is reflected across the -axis?

Possible Answers:

Correct answer:

Explanation:

To find the reflected image of the triangle, first identify how it is being reflected. This particular problem states that it is being reflected over the -axis. Recall that the -axis is the horizontal axis on the coordinate grid and is equivalent to the line .

Plot the points of the original triangle on the coordinate grid.

Screen shot 2016 06 15 at 6.33.25 am

From here, to reflect the image across the -axis take the negative of all the  values.

This change results in the following,

Screen shot 2016 06 15 at 6.40.50 am

Therefore, the reflected triangle has coordinates at

Example Question #51 : High School: Geometry

A rectangle's coordinate points are , , , and . If the rectangle is translated down seven units what are the coordinates of the translated rectangle?

Possible Answers:

Correct answer:

Explanation:

To find the coordinates of the translated rectangle, first recall what a translation is. A translation is a shift of the original object without changing the shape of size of the object. In this particular case the starting coordinates of the rectangle are given and the goal is to move the rectangle down seven units. A shift down means a algebraic change in the  coordinate.

The original rectangle is

Screen shot 2016 06 15 at 7.46.37 am

If each point on the rectangle is shifted down seven units it results in the following

Screen shot 2016 06 15 at 7.57.18 am

Therefore, the coordinate points of the translated rectangle are

These coordinates can also be found algebraically by subtracting seven from each  value.

Example Question #12 : Drawing Transformed Figures: Ccss.Math.Content.Hsg Co.A.5

A rectangle's coordinate points are , , , and . If the rectangle is translated up  units and to the right  units what are the coordinates of the translated rectangle?

Possible Answers:

Correct answer:

Explanation:

To find the coordinates of the translated rectangle, first recall what a translation is. A translation is a shift of the original object without changing the shape of size of the object. In this particular case the starting coordinates of the rectangle are given and the goal is to move the rectangle up two units and to the right 5 units. A shift up means a algebraic change in the  coordinate and a shift to the right means an algebraic change to the  coordinate.

The original rectangle is

Screen shot 2016 06 15 at 7.46.37 am
If each point on the rectangle is shifted up two units and to the right five units results in the following

Screen shot 2016 06 15 at 8.32.40 am

Therefore, the coordinate points of the translated rectangle are

All Common Core: High School - Geometry Resources

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