Translations

Front

What is a translation in geometry?

Back

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

Front

How do you represent a translation mathematically?

Back

A translation can be represented by a rule such as (x, y) → (x + a, y + b), where 'a' and 'b' are the horizontal and vertical shifts, respectively.

Front

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

Back

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

Front

If a point M has coordinates (-3, 5) and is translated using the rule (x, y) → (x - 1, y), what are the new coordinates?

Back

The new coordinates of M' would be (-4, 5).

Front

How do you translate a point 3 units to the left and 9 units down?

Back

You would apply the translation rule (x, y) → (x - 3, y - 9).

Front

What is the effect of translating a triangle on its vertices?

Back

Translating a triangle moves all its vertices the same distance and in the same direction, preserving the shape and size.

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.

Front

How can you determine the translation needed to move triangle A'B'C' to triangle ABC?

Back

You can find the translation by calculating the difference in coordinates between corresponding vertices of the two triangles.

Front

What are the coordinates of point X after translating it 3 units left and 9 units down from (1, 4)?

Back

The new coordinates of X' would be (-2, -5).

Front

What is the general form of a translation vector?

Back

A translation vector is generally expressed as (a, b), where 'a' is the horizontal shift and 'b' is the vertical shift.