Translations

Front

What is a translation in geometry?

Back

A translation is a type of transformation that moves every point of a shape or object a certain distance in a specified direction without changing its size, shape, or orientation.

Front

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

Back

This rule represents a translation of a point (x, y) by 'a' units in the x-direction and 'b' units in the y-direction.

Front

What is the result of translating the point (3, 4) by the vector (2, -3)?

Back

The new point after translation is (3 + 2, 4 - 3) = (5, 1).

Front

What does it mean for translations to be congruent?

Back

Congruent means that the original shape and the translated shape are identical in size and shape; they are simply in different locations.

Front

If a point (x, y) is translated to (x + 6, y - 1), what is the translation vector?

Back

The translation vector is (6, -1).

Front

How do you write the translation rule for moving a shape 4 units left and 3 units down?

Back

The translation rule is (x, y) → (x - 4, y - 3).

Front

What is the translation of the point (1, 2) using the rule (x, y) → (x + 5, y + 2)?

Back

The new point after translation is (1 + 5, 2 + 2) = (6, 4).

Front

What is the effect of translating a triangle by a vector of (0, 5)?

Back

The triangle will move vertically upwards by 5 units without changing its shape or orientation.

Front

If triangle ABC has vertices A(1, 2), B(3, 4), and C(5, 6), what are the new coordinates after translating by (-2, 3)?

Back

The new coordinates will be A(-1, 5), B(1, 7), and C(3, 9).

Front

What is the translation rule for moving a shape 10 units right and 5 units up?

Back

The translation rule is (x, y) → (x + 10, y + 5).