Translations & Reflections on the Coordinate Plane

Front

What is a translation in the coordinate plane?

Back

A translation is a transformation that slides a figure a certain distance in a specified direction without changing its shape or orientation.

Front

How do you represent a translation mathematically?

Back

A translation can be represented by the rule (x, y) → (x + a, y + b), where 'a' is the horizontal shift and 'b' is the vertical shift.

Front

What does it mean to reflect a figure over the x-axis?

Back

Reflecting a figure over the x-axis means that for every point (x, y) in the figure, the corresponding point after reflection will be (x, -y).

Front

What does it mean to reflect a figure over the y-axis?

Back

Reflecting a figure over the y-axis means that for every point (x, y) in the figure, the corresponding point after reflection will be (-x, y).

Front

What is the effect of a reflection on the coordinates of a point?

Back

A reflection changes the sign of the coordinate that is perpendicular to the axis of reflection while keeping the other coordinate the same.

Front

What transformation is represented by the rule (x, y) → (x + 2, y - 3)?

Back

This transformation is a translation that slides the figure 2 units to the right and 3 units down.

Front

What is the difference between a translation and a reflection?

Back

A translation moves a figure without changing its orientation, while a reflection flips a figure over a line, changing its orientation.

Front

What is the definition of a reflection in geometry?

Back

A reflection is a transformation that creates a mirror image of a figure over a line (axis) in the coordinate plane.

Front

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

Back

The x-coordinate changes sign, while the y-coordinate remains the same.

Front

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

Back

The y-coordinate changes sign, while the x-coordinate remains the same.