Transformations

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in a specified direction.

Front

How do you represent a translation mathematically?

Back

A translation can be represented by a rule such as (x, y) → (x+a, y+b), where 'a' and 'b' are the distances moved in the x and y directions, respectively.

Front

What does the rule (x, y) → (x+3, y-2) indicate about the translation of a figure?

Back

It indicates that the figure is moved 3 units to the right and 2 units down.

Front

What is a reflection in geometry?

Back

A reflection is a transformation that flips a figure over a line, creating a mirror image.

Front

How is a reflection across the x-axis represented mathematically?

Back

A reflection across the x-axis is represented by the rule (x, y) → (x, -y).

Front

What is the result of reflecting a point (3, 4) across the x-axis?

Back

The result is the point (3, -4).

Front

What is the effect of translating a point (2, 5) by the rule (x-2, y+6)?

Back

The point will move 2 units left and 6 units up, resulting in the new point (0, 11).

Front

What does the term 'transformation' refer to in geometry?

Back

A transformation refers to any operation that alters the form, position, or size of a figure.

Front

What is the new position of point T(2, -5) after translating it 3 units to the right and 6 units up?

Back

The new position of point T' would be (5, 1).

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.