translations

Front

What is a translation in geometry?

Back

A translation is a type of 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 as (x, y) → (x + a, y + b), where 'a' is the horizontal shift and 'b' is the vertical shift.

Front

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

Back

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

Front

If a point (2, 5) is translated using the rule (x, y) → (x - 1, y + 4), what are the new coordinates?

Back

The new coordinates are (1, 9).

Front

What is the effect of a translation on the shape of a figure?

Back

A translation does not change the shape, size, or orientation of a figure; it only changes its position.

Front

Describe the translation represented by (x, y) → (x + 4, y).

Back

This represents a translation 4 units to the right, with no vertical movement.

Front

What are the coordinates of the point (3, 2) after a translation of 5 units left and 3 units up?

Back

The new coordinates are (-2, 5).

Front

How can you determine the direction of a translation from a rule?

Back

The direction can be determined by the signs of 'a' and 'b' in the rule (x, y) → (x + a, y + b): positive 'a' means right, negative 'a' means left; positive 'b' means up, negative 'b' means down.

Front

What is the translation rule for moving a point 2 units down and 3 units left?

Back

The translation rule is (x, y) → (x - 3, y - 2).

Front

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

Back

The new coordinates are A(3, 1), B(5, 3), and C(7, 5).