Translations

Slide figures while preserving distance and angle measure.

Lesson 1 of 53 parts Practice Flashcards

1/3

Translation Rules

Objective: Apply a translation rule to a point or figure.

A translation maps every point $(x, y)$ of a figure to $(x + a, y + b)$ for fixed real numbers $a$ and $b$ , preserving distance and angle measure.

Formulas

Worked examples

Try itTranslate

(3, -1)

(x, y) \mapsto (x + 4, y + 5)

.Show answer

$(3 + 4, -1 + 5) = (7, 4)$

Swipe sideways to move between sections

Objective: Apply a translation rule to a point or figure.

A translation maps every point $(x, y)$ of a figure to $(x + a, y + b)$ for fixed real numbers $a$ and $b$ , preserving distance and angle measure.

Formulas

Worked examples

Try itTranslate

(3, -1)

(x, y) \mapsto (x + 4, y + 5)

.Show answer

$(3 + 4, -1 + 5) = (7, 4)$

Objective: Determine a translation vector from corresponding points.

If P(x,y) maps to P′(u,v), the translation vector is (u−x,v−y); apply it to all vertices.

Objective: Recognize preserved measures and orientation.

Translations are rigid motions: corresponding lengths and angles remain equal and orientation is preserved. A translation by (0,0) is the identity.

You finished the reading!

Lock it in with a few practice questions, then move on to the next lesson.