Exploring Transformed Figures: Rotations and Reflections

What does the term 'rigid motions' imply in geometry?

• Translations that result in a change of orientation

• Rotations that only occur in a clockwise direction

• Movements that keep the figure congruent to its original form

• Transformations that change the shape and size of figures

Which transformation does not alter the size of a figure?

• Scaling

• Translation

• Reflection

• Dilation

What is a translation in geometry?

• Flipping a figure over a line

• Sliding a figure left, right, up, or down

• Changing the size of a figure

• Rotating a figure around a point

What formula represents a translation in geometry?

• x + a, y + b

• x - a, y - b

• a - x, b - y

• a + x, b + y

What happens to a figure during a 90-degree counterclockwise rotation?

• The x and y coordinates remain the same, but their signs change

• The figure is flipped over the x-axis

• The figure is enlarged by a factor of 90

• The x and y coordinates switch places, and the sign of y changes

What is the effect of a 180-degree counterclockwise rotation on a figure's coordinates?

• The y-coordinate changes sign, and the x-coordinate remains the same

• Both coordinates switch places

• Both coordinates change their signs

• The x-coordinate changes sign, and the y-coordinate remains the same

How does a figure change when reflected over the y-axis?

• Both coordinates change their signs

• Both coordinates switch places

• The y-coordinate changes sign

• The x-coordinate changes sign

When reflecting a figure over the line y = x, what happens to the coordinates?

• The y-coordinate changes sign

• The x-coordinate changes sign

• The coordinates change their signs

• The coordinates switch places

What is the result of reflecting a point over the x-axis and then rotating it 90 degrees counterclockwise?

• The point's x-coordinate becomes positive, and the y-coordinate becomes negative

• The point returns to its original position

• The point's x and y coordinates switch places, with the original y-coordinate changing sign

• The point moves to a new position with both coordinates changing signs

After reflecting a point over the x-axis, what happens to the y-coordinate?

• It remains unchanged

• It increases by the same amount it was above the x-axis

• It changes sign

• It becomes zero