Translations

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a shape a certain distance in a specified direction.

Front

How do you represent a translation mathematically?

Back

A translation can be represented as (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 to the right?

Back

It means to add 5 to the x-coordinate of every point in the shape.

Front

If a point (2, 3) is translated 3 units left and 2 units down, what is the new position?

Back

The new position is (-1, 1).

Front

What is the effect of translating a shape 0 units horizontally and 4 units vertically?

Back

The shape will move straight up by 4 units without changing its horizontal position.

Front

How do you find the new coordinates after a translation?

Back

Add the translation values to the original coordinates: New x = original x + horizontal shift, New y = original y + vertical shift.

Front

What is the translation vector for moving a shape 6 units down and 2 units to the left?

Back

The translation vector is (-2, -6).

Front

If triangle ABC is translated to triangle A'B'C' using the vector (x + 4, y - 3), what is the direction of the translation?

Back

The triangle is translated 4 units to the right and 3 units down.

Front

What does the notation (x, y) → (x + 2, y - 3) indicate?

Back

It indicates a translation of 2 units to the right and 3 units down.

Front

If a point (5, 5) is translated 8 units right and 3 units up, what are the new coordinates?

Back

The new coordinates are (13, 8).