L7 · Translations on the Cartesian plane

Learning goal

“I can translate a point or a whole polygon on the Cartesian plane, describe the translation in words ('right a, up b'), write it as (x + a, y + b), and track every vertex to its image.”

Translation — a slide: moving a shape without turning or flipping it; every point moves the same distance in the same direction.

Image — the shape or point after a transformation; written with a prime mark, like A' ("A prime").

Prime mark — the small mark added to a point's name after it has been transformed (A becomes A').

Vector (of a translation) — the pair of moves that describes a slide: how far right (or left) and how far up (or down) every point travels.

Worked example

Point A (3, 4) is translated 4 right and 1 up. Find A'. Step 1: Right adds to x: 3 + 4 = 7. Step 2: Up adds to y: 4 + 1 = 5. Step 3: A' = (7, 5). The translation is written (x + 4, y + 1): whatever point (x, y) you start with, add 4 to its x and 1 to its y. Left and down subtract instead: 2 left and 3 down is (x - 2, y - 3).

Check yourself — explain it

Translating a point 5 left changes...

Paired problem — example still visible

Point B (6, 2) is translated 3 left and 4 up. Find B'. -> (3, 6) (x: 6 - 3 = 3; y: 2 + 4 = 6).

Faded completion — last step is yours

"Point C (5, 7) is translated 2 right and 3 down: C' = (5 + 2, 7 - 3) = ( ___, ___ )" -> (7, 4)

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz