Translations Flashcards

All 6 cards in this deck

In a translation vector $\binom{a}{b}$, what do the top and bottom numbers tell you?

e.g. $\binom{3}{-2}$

Top = movement parallel to the $x$-axis (positive = right), bottom = movement parallel to the $y$-axis (positive = up).

e.g. 3 right and 2 down.

What must you state to describe fully a translation?

Translation, and the column vector, e.g. translation by vector $\binom{-5}{6}$ (not the coordinate $(-5,6)$).

True or false? A translation can change the size or orientation of a shape.

False. The image is congruent to the object and has the same orientation; only its position changes.

What are the steps to translate a shape on a grid by a given vector?

e.g. translate by $\binom{-1}{-2}$

1. Pick a vertex and count the vector across then up/down: 1 left, 2 down.
2. Plot the image of that vertex, then repeat for every vertex.
3. Join the image vertices in the same order and label the image.

What happens to the centre and radius of a circle when the circle is translated by a vector?

e.g. $x^2+y^2=16$ translated by $\binom{3}{0}$

The centre moves by the vector; the radius is unchanged.

e.g. centre $(3,0)$, radius $4$.

What single transformation maps the image back onto the object after a translation by vector $\binom{a}{b}$?

e.g. translation by $\binom{4}{-1}$

Translation by $\binom{-a}{-b}$.

e.g. translation by $\binom{-4}{1}$.