Translations Flashcards

All 3 cards in this deck

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.