Translations

Front

What is a translation in geometry?

Back

A translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.

Front

How is a translation represented in coordinate notation?

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 the notation (x, y) --> (x + 2, y + 5) indicate?

Back

It indicates a translation of 2 units to the right and 5 units up.

Front

If a point A is at (3, 2), where will it be after a translation of 4 units left and 3 units down?

Back

A' will be at (-1, -1).

Front

What is the effect of a translation of (x, y) --> (x - 5, y) on a point?

Back

It moves the point 5 units to the left, keeping the y-coordinate the same.

Front

What is the result of translating a triangle with vertices A(1, 1), B(2, 2), and C(3, 3) by (x + 3, y - 2)?

Back

The new vertices will be A'(4, -1), B'(5, 0), and C'(6, 1).

Front

What does the transformation (x, y) --> (x, y + 4) do to a point?

Back

It translates the point 4 units up.

Front

How do you translate a point 2 units right and 3 units down?

Back

Use the transformation (x, y) --> (x + 2, y - 3).

Front

What is the difference between a translation and a reflection?

Back

A translation moves a shape without changing its orientation, while a reflection flips a shape over a line.

Front

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

Back

The corresponding points A, B, C and A', B', C' are congruent and maintain the same shape and size.