Translations and Reflections Quiz

What is a reflection in geometry?

• A reflection in geometry is a transformation that rotates a figure around a point.

• A reflection in geometry is a transformation that stretches or shrinks a figure.

• A reflection in geometry is a transformation that slides a figure along a line.

• A reflection in geometry is a transformation that flips a figure over a line called the line of reflection.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Which of the following is an example of a reflection?

• Sound traveling through air

• Heat transferring from a hot object to a cold object

• A ball bouncing off a wall

• Light bouncing off a mirror

True or False: A reflection is a transformation that flips a figure over a line.

• False

• A reflection is a transformation that rotates a figure

• A reflection is a transformation that stretches a figure

• True

What is the line of reflection?

• The line of reflection is the mirror line.

• The line of reflection is the rotation axis.

• The line of reflection is the perpendicular bisector.

• The line of reflection is the axis of symmetry.

Answer explanation

The line of reflection, also known as the mirror line, is the correct choice. It is the line over which a figure is reflected to create a mirror image. The other options, rotation axis, perpendicular bisector, and axis of symmetry, are not the same as the line of reflection.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Which of the following is an example of a figure that has undergone a reflection?

• Circle

• Triangle

• Number '7'

• Letter 'D'

Answer explanation

A reflection is a transformation that flips a figure over a line, creating a mirror image. Among the given options, the letter 'D' is an example of a figure that has undergone a reflection, as it can be divided into two symmetrical halves by a vertical line.

True or False: A reflection preserves the size and shape of a figure.

• False

• A reflection changes the size but preserves the shape

• A reflection changes the shape but preserves the size

• True

Answer explanation

True. A reflection is a type of transformation that flips a figure over a line, creating a mirror image. It preserves the size and shape of the figure, as all the angles and side lengths remain the same after the reflection.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What are the coordinates of a point after a reflection over the x-axis?

• (x, -y)

• (-x, y)

• (x, y)

• (-x, -y)

Answer explanation

The reflection of a point over the x-axis changes the sign of the y-coordinate while keeping the x-coordinate the same. Therefore, if the original point is (x, y), after reflection over the x-axis, the coordinates become (x, -y). This is why the correct answer is (x, -y).

What are the coordinates of a point after a reflection over the y-axis?

• (x, y)

• (y, -x)

• (x, -y)

• (-x, y)

Answer explanation

The reflection of a point over the y-axis changes the sign of the x-coordinate while keeping the y-coordinate the same. Therefore, if the original point is (x, y), after reflection over the y-axis, it becomes (-x, y). This is why the correct answer is (-x, y).

What is the result of reflecting a figure twice over the same line?

• The result is a figure that is translated to a different location.

• The result is a figure that is scaled to a different size.

• The result is a figure that is rotated 180 degrees.

• The result is the original figure.

Answer explanation

The question asks about the result of reflecting a figure twice over the same line. The correct answer is that the result is the original figure. This is because when a figure is reflected twice over the same line, it returns to its original position, maintaining its original shape and size. Therefore, the figure remains the same as it was before the reflections.

True or False: A reflection is a rigid transformation.

• Not applicable

• Partially true

• False

• True

Answer explanation

The statement in the question is true. A reflection is indeed a rigid transformation. In mathematics, a rigid transformation (also called an isometry) is a transformation of a space that preserves distances and angles. Reflections, rotations, and translations are all examples of rigid transformations.