Translations

Front

What is a translation in geometry?

Back

A translation is a type of transformation that moves every point of a shape a certain distance in a specified direction without changing its size, shape, or orientation.

Front

How do you represent a translation mathematically?

Back

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

Front

What does it mean to translate a shape 5 units down and 3 units to the right?

Back

It means to move every point of the shape 5 units down on the y-axis and 3 units to the right on the x-axis.

Front

If a point is translated from (2, 3) to (5, 8), what is the translation rule?

Back

The translation rule is (x, y) → (x + 3, y + 5).

Front

What is the effect of translating a shape on its area?

Back

The area of the shape remains unchanged after a translation.

Front

How do you translate a point 4 units left and 2 units down?

Back

The translation rule is (x, y) → (x - 4, y - 2).

Front

What is the translation rule for moving a point 6 units right and 1 unit down?

Back

The translation rule is (x, y) → (x + 6, y - 1).

Front

If triangle A'B'C' is translated to triangle ABC, what does this imply about their positions?

Back

It implies that triangle ABC is the result of moving triangle A'B'C' to a new location without changing its shape or size.

Front

What is the difference between translation and rotation?

Back

Translation moves a shape without changing its orientation, while rotation turns a shape around a fixed point.

Front

What happens to the coordinates of a point when it is translated?

Back

The coordinates of the point change according to the translation rule, reflecting the distance and direction of the movement.