Translations

Front

What is a translation in geometry?

Back

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

Front

What does the notation (x, y) --> (x + a, y + b) represent?

Back

It represents a translation of a point (x, y) by 'a' units horizontally and 'b' units vertically.

Front

If a point (3, 4) is translated using (x, y) --> (x + 2, y - 3), what is the new position?

Back

(5, 1)

Front

What is the relationship between the preimage and image in a translation?

Back

The preimage and image are congruent; they have the same shape and size.

Front

How do you translate a triangle A'B'C' to triangle ABC if the translation is (x - 2, y + 5)?

Back

You subtract 2 from the x-coordinates and add 5 to the y-coordinates of each vertex.

Front

What is the effect of translating a figure 3 units to the right and 2 units down?

Back

The new coordinates of any point (x, y) will be (x + 3, y - 2).

Front

If triangle ABC is at (1, 2), (3, 4), (5, 6), where will it be after a translation of (x + 4, y - 1)?

Back

The new coordinates will be (5, 1), (7, 3), (9, 5).

Front

What does it mean for two figures to be congruent after a translation?

Back

It means they have the same size and shape, even though their positions may differ.

Front

If a triangle is translated using (x + 2, y - 3), what is the direction of the translation?

Back

The triangle is moved 2 units to the right and 3 units down.

Front

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

Back

By finding the difference in coordinates between corresponding points of the triangles.