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

What does the rule (x, y) → (x + a, y + b) represent?

Back

This rule represents a translation where 'a' is the horizontal shift and 'b' is the vertical shift.

Front

If a point P(2, 3) is translated 4 units to the right and 2 units up, what are the new coordinates?

Back

P'(6, 5)

Front

What is the pre-image in a transformation?

Back

The pre-image is the original figure before any transformation is applied.

Front

What is the image in a transformation?

Back

The image is the resulting figure after a transformation has been applied.

Front

How do you translate a point 3 units left and 5 units down?

Back

Use the rule (x, y) → (x - 3, y - 5).

Front

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

Back

The figure remains unchanged; it is still in the same position.

Front

If triangle ABC is translated using the rule (x, y) → (x + 2, y - 3), what happens to the triangle?

Back

Each vertex of triangle ABC moves 2 units to the right and 3 units down.

Front

What is the transformation from point (1, 1) to (4, 5)?

Back

The transformation is a translation of 3 units to the right and 4 units up.

Front

What is the difference between a translation and a rotation?

Back

A translation moves a figure without changing its orientation, while a rotation turns a figure around a fixed point.