Translations

Front

What is a translation in geometry?

Back

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

Front

How do you represent a translation algebraically?

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 happens to the coordinates of a point (x, y) when it is translated 5 units left and 2 units up?

Back

The new coordinates will be (x - 5, y + 2).

Front

If a point (3, 4) is translated according to the rule (x, y) → (x + 2, y - 3), what are the new coordinates?

Back

The new coordinates will be (5, 1).

Front

What is the effect of translating a point (x, y) by (0, 0)?

Back

The point remains unchanged; it stays at (x, y).

Front

Describe the translation (x, y) → (x - 4, y + 6).

Back

This translation moves the point 4 units left and 6 units up.

Front

What is the image of the point (1, 2) under the translation (x, y) → (x + 3, y - 5)?

Back

The image is (4, -3).

Front

If a triangle ABC has vertices A(1, 2), B(3, 4), and C(5, 6), what are the coordinates after a translation of (x + 2, y - 1)?

Back

The new vertices will be A(3, 1), B(5, 3), and C(7, 5).

Front

What does the translation (x, y) → (x + 5, y) do to a point?

Back

It moves the point 5 units to the right without changing its vertical position.

Front

If a point is translated 10 units down, how is this represented algebraically?

Back

This is represented as (x, y) → (x, y - 10).