Translations

Front

What is a translation in geometry?

Back

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

Front

How do you represent a translation mathematically?

Back

A translation can be represented as (x, y) → (x + a, y + b), where (a, b) is the vector that indicates the direction and distance of the translation.

Front

What does the translation rule (x + 2, y - 5) indicate?

Back

This rule indicates that every point of the shape is moved 2 units to the right and 5 units down.

Front

If point M (-3, 5) is translated using the rule (x, y) → (x - 1, y - 4), what are the new coordinates?

Back

The new coordinates of M' are (-4, 1).

Front

What does it mean to translate a shape 5 units to the right and 8 units down?

Back

It means to move every point of the shape 5 units in the positive x-direction and 8 units in the negative y-direction.

Front

How can you identify the translation from triangle ABC to triangle A'B'C'?

Back

By comparing the coordinates of corresponding points in both triangles and determining the changes in x and y values.

Front

What is the effect of the translation rule (x, y) → (x + 4, y + 8)?

Back

This rule translates a point 4 units to the right and 8 units up.

Front

What is the translation vector for moving a shape 3 units left and 2 units up?

Back

The translation vector is (-3, 2).

Front

If trapezoid ABCD is translated 5 units to the right and 5 units down, what is the new position of point A (2, 3)?

Back

The new position of point A will be (7, -2).

Front

What transformation occurs when the rule (x, y) → (x - 2, y + 3) is applied?

Back

This transformation slides the shape 2 units to the left and 3 units up.