Geometry
Translation
A translation slides every point of a figure the same distance in the same direction. It is described as (x + a, y + b) — add a to every x-coordinate and b to every y-coordinate.
Visualize It
Translation slides every point the same distance
Watch & Learn
Watch a clear, friendly video explanation of Translation:
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Translate point (3, 5) by (x + 2, y − 3)
Point (3,5) → (5,2)
Step-by-Step Solution
Add 2 to x: 3 + 2 = 5
Subtract 3 from y: 5 − 3 = 2
New point: (5, 2)
Answer
(5, 2)
Problem
Triangle has vertices (1,1), (3,1), (2,4). Translate by (x−2, y+1).
Translate (x−2, y+1)
Step-by-Step Solution
(1,1) → (1−2, 1+1) = (−1, 2)
(3,1) → (3−2, 1+1) = (1, 2)
(2,4) → (2−2, 4+1) = (0, 5)
Answer
(−1,2), (1,2), (0,5)
Problem
A point moves from (4, −2) to (7, 1). What is the translation rule?
(4,−2) → (7,1)
Step-by-Step Solution
Change in x: 7 − 4 = +3
Change in y: 1 − (−2) = +3
Translation: (x + 3, y + 3)
Answer
(x + 3, y + 3)
Problem
Translate the point (−5, 3) by (x + 6, y − 4)
(−5,3) → (1,−1)
Step-by-Step Solution
Add 6 to x: −5 + 6 = 1
Subtract 4 from y: 3 − 4 = −1
New point: (1, −1)
Answer
(1, −1)
Problem
A triangle has vertices (0, 0), (4, 0), (2, 3). After translation (x − 3, y + 2), what are the new vertices?
Translate (x−3, y+2)
Step-by-Step Solution
(0, 0) → (0−3, 0+2) = (−3, 2)
(4, 0) → (4−3, 0+2) = (1, 2)
(2, 3) → (2−3, 3+2) = (−1, 5)
Answer
(−3, 2), (1, 2), (−1, 5)
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Translate (2, 6) by (x + 4, y − 5)
Translate (−3, 2) by (x − 1, y + 4)
Point moves from (1, 3) to (5, 7). Translation rule?
Translate (0, 0) by (x − 3, y + 2)
Translate (5, −1) by (x + 0, y − 3)
Translate (−2, −4) by (x + 5, y + 5)
Point moves from (3, 7) to (3, 2). Translation rule?
Translate (4, 4) by (x − 4, y − 4)
Translate (−1, 5) by (x + 3, y − 8)
Point moves from (0, 0) to (−6, 4). Translation rule?
Translate (10, −3) by (x − 10, y + 3)
Translate (−5, −5) by (x + 5, y + 5)
Finished all 12? Give yourself a pat on the back — then check your work!
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