### All Common Core: High School - Geometry Resources

## Example Questions

### Example Question #41 : Congruence

If a triangle is in quadrant three and undergoes a transformation that moves each of its coordinate points to the left three units and down one unit, what transformation has occurred?

**Possible Answers:**

Translation

Reflection

None of the other answers.

Extension

Rotation

**Correct answer:**

Translation

To determine the type of transformation that is occurring in this particular situation, first recall the different types of 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.

Since each of the triangle's coordinates is moved to the left and down, it is seen that the size and shape of the triangle remains the same but its location is different. Therefore, the transformation the triangle has undergone is a translation.

### Example Question #43 : Congruence

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

**Possible Answers:**

Rotations

Reflection

Non of the others

Extension

Dilation

**Correct answer:**

Reflection

"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 #1 : 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

Rotation

None of the other answers.

Extension

Dilation

**Correct answer:**

Reflection

"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:**

Reflection

Rotation

Dilation

None of the other answers.

Translation

**Correct answer:**

Translation

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 #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:**

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.

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

This change results in the following,

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:**

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.

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

This change results in the following,

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 and -axis?

**Possible Answers:**

**Correct answer:**

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.

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,

Therefore, the coordinates of the reflected trapezoid are

### Example Question #51 : Congruence

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:**

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.

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

This change results in the following,

Therefore, the reflected triangle has coordinates at

### 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 triangle after it is reflected across the and -axis?

**Possible Answers:**

**Correct answer:**

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.

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,

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:**

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.

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

This change results in the following,

Therefore, the reflected triangle has coordinates at