Translations Flashcards

All 4 cards in this deck

What does the column vector $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$ tell you about a translation?

Move 3 units right and 2 units down.
Top number = horizontal (right if positive), bottom number = vertical (up if positive).

What are the steps to translate a shape by a column vector?
e.g. translate by $\begin{pmatrix} 4 \\ -1 \end{pmatrix}$

1. Read the vector: 4 right, 1 down.
2. Move every vertex 4 right and 1 down.
3. Join the new vertices — the image is the same size and shape.

What must you state to fully describe a translation?

The word "translation" and the column vector.
e.g. translation by $\begin{pmatrix} 5 \\ -4 \end{pmatrix}$

Which properties of a shape are unchanged by a translation?

Lengths, angles and orientation are all unchanged — only the position changes.
The image is congruent to the object.