Translations

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 translate a point (x, y) to the right by a units?

Back

To translate a point (x, y) to the right by a units, you add a to the x-coordinate: (x + a, y).

Front

How do you translate a point (x, y) down by b units?

Back

To translate a point (x, y) down by b units, you subtract b from the y-coordinate: (x, y - b).

Front

What is the result of translating point P(3, 4) 2 units to the right and 3 units down?

Back

The new point P' will be (3 + 2, 4 - 3) = (5, 1).

Front

If a point is translated 5 units down and 4 units to the right, what is the transformation rule?

Back

The transformation rule is (x, y) → (x + 4, y - 5).

Front

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

Back

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

Front

How do you find the new coordinates of a point after translation?

Back

Add the translation values to the original coordinates: (x + a, y + b).

Front

What is the effect of translating a shape on its size and orientation?

Back

Translating a shape does not change its size or orientation; it only changes its position.

Front

If trapezoid ABCD is translated 8 units down and 5 units to the right, what are the new coordinates of point A(1, 2)?

Back

The new coordinates of point A will be (1 + 5, 2 - 8) = (6, -6).

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.