Exploring Translations, Rotations, and Reflections

The video tutorial covers transformations including translations, rotations, and reflections. The teacher guides students through solving problems related to these transformations, explaining key concepts such as labeling figures, understanding quadrants, and preserving orientation. The tutorial also discusses algebraic representations and coordinate transformations, providing a comprehensive overview of the topic.

What type of transformation involves a figure turning around a point?

• Translation

• Reflection

• Rotation

• Dilation

If a figure is moved from one position to another without turning, what is this transformation called?

• Scaling

• Reflection

• Rotation

• Translation

Which transformation does not change the orientation of a figure?

• Rotation

• Shearing

• Translation

• Reflection

What is the result of a reflection transformation over the y-axis?

• The x-coordinates change signs

• The y-coordinates change signs

• Both coordinates change signs

• No coordinates change signs

What is the algebraic representation for a reflection over the x-axis?

• (x, -y)

• (-y, -x)

• (-x, y)

• (y, x)

Which transformation is described by the rule (x, y) -> (x - 7, y + 6)?

• Translation 7 units right and 6 units up

• Translation 7 units right and 6 units down

• Translation 7 units left and 6 units up

• Translation 7 units left and 6 units down

What does a 270-degree clockwise rotation do to the coordinates (x, y)?

• (-y, x)

• (y, -x)

• (x, -y)

• (-x, y)

What transformation is represented by the rule (x, y) -> (-y, x)?

• 180-degree rotation

• 270-degree clockwise rotation

• 90-degree clockwise rotation

• 90-degree counterclockwise rotation

If a figure is rotated 100 degrees clockwise, which of the following is true?

• The x and y coordinates switch and y becomes negative

• Both coordinates become their opposites

• The x and y coordinates switch and x becomes negative

• No change in coordinates

Which statement is true for a figure after a 90-degree counterclockwise rotation?

• None of the above

• It mirrors over the y-axis

• It mirrors over the x-axis

• It aligns with a 270-degree clockwise rotation