Unit 4.1 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

How do you describe a translation mathematically?

Back

A translation can be described using a rule in the form (x + a, y + b), where 'a' is the horizontal shift and 'b' is the vertical shift.

Front

What does the term 'pre-image' refer to in transformations?

Back

The pre-image is the original figure before any transformation is applied.

Front

If a point A is translated 3 units to the right and 4 units down, what is the new position of point A if its original coordinates are (2, 5)?

Back

The new position of point A would be (5, 1).

Front

What is the effect of translating a figure 0 units horizontally and 0 units vertically?

Back

The figure remains unchanged; it is effectively the same as not performing any translation.

Front

How do you find the coordinates of a translated point?

Back

To find the coordinates of a translated point, apply the translation rule to the original coordinates.

Front

What is the result of translating a triangle with vertices A(1, 2), B(3, 4), and C(5, 6) by the rule (x + 2, y - 3)?

Back

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

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

If triangle A'B'C' is translated to triangle ABC using the rule (x + 2, y - 9), what is the translation vector?

Back

The translation vector is (2, -9).

Front

What does it mean to translate a figure '8 units right and 6 units down'?

Back

It means to move every point of the figure 8 units in the positive x-direction and 6 units in the negative y-direction.