5C: Reflections

What is a reflection?

• When you turn an object around a point.

• When you slide an object form one place to another.

• When you flip or mirror an object across a line.

• When you resize an object.

Answer explanation

A reflection is when a figure is flipped or mirrored across a particular line.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What axis is the triangle being reflected over?

• X-axis

• Y-axis

Answer explanation

Think of your axis of reflection as a book spine: If you "turn the page" to move your figure from preimage to image, where would the page have been attached?

In this case, the y-axis.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What axis is the image reflected over?

• X-axis

• Y-axis

Answer explanation

Think of your axis of reflection as a book spine: If you "turn the page" to move your figure from preimage to image, where would the page have been attached?

In this case, the x-axis.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Reflections over the x-axis change the ____-__________.

• y-coordinate

• x-coordinate

Answer explanation

If you compare the points in the visual example, you can see that the x-values are the same but the sign of the y-value was changed.

Therefore, reflecting over the x-axis changes the y-coordinate.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What would be the coordinates of point K if it was reflected over the x-axis?

• (-5, -2)

• (-5, 2)

• (5, -2)

Answer explanation

Think of your axis of reflection as a book spine: If you "turn the page" to transform your figure, with the page attached to the x-axis, where does point K' end up?

(-5,2) on the other side of the x-axis

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Which answer shows a reflection across the x-axis?

• a

• b

• c

• d

Answer explanation

Figure A shows a reflection across the line y=x.

Figure B shows a rotation.

Figure C shows a reflection across the x-axis.

Figure D Shows a reflection across the y-axis.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Identify the transformation from ABC to A'B'C'.

• 90^o clockwise rotation

• 90^o counter clockwise rotation

• Reflection across the y-axis

• Reflection across the x-axis

Answer explanation

The image appears to be flipped from the preimage, which indicates a reflection.

The figure would need to be flipped/reflected across the x-axis to be oriented the way it is. Think of it like a page turned from preimage to image, with the page "attached" at the x-axis.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Which correctly describes the two transformations that were used to create the image on the graph?

• Reflection over the y-axis and a rotation 90^o counter clockwise

• (x+10, y) and reflection over x-axis

• Rotation 90^o clockwise and a reflection over the x-axis

• Reflection over the x-axis ad a translation (x+6,y)

Answer explanation

A reflection over the y-axis would flip the order of the labels. Then, a 90 degree counterclockwise rotation would turn the figure on it's side.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Which series of transformations were performed in the figure?

• Translation 5 units down, reflection over the y-axis

• Reflection over the x-axis, translation 6 units right

• Rotation 90^o clockwise, reflection over the x-axis

• Rotation 180^o clockwise, reflection over the y-axis

Answer explanation

A 90 degree clockwise rotation would turn the figure on its side.

Then, a reflection across the x-axis would flip the figure to map to the final image.

Tags

CCSS.8.G.A.3

Describe a sequence of transformations that maps figure A onto figure B.

• A translation 4 units right followed by a reflection across the x-axis

• A reflection across the x-axis followed by a reflection across the y-axis

• A reflection across the y-axis followed by a translation 6 units down

• A 90° counterclockwise rotation about the Origin followed by a reflection across the y-axis

Answer explanation

One step that would take figure A to figure B is a 180 degree rotation. This is the same as a reflection over the x-axis followed by a reflection across the y-axis.

Tags

CCSS.8.G.A.3