Definition: A translation is a transformation that slides every point of a figure the same distance in the same direction without turning or flipping it.
What is a translation?
It is a slide. Every point moves along parallel paths by the same amount, so the image is an exact copy in a new position.
How do you write one?
Use a rule: (x, y) becomes (x + a, y + b). Positive a moves right and negative moves left. Positive b moves up and negative moves down.
What does it look like?
Triangle ABC has vertices A(1, 2), B(4, 2), C(3, 6). Translate by (x – 5, y + 3):
- A’ = (-4, 5)
- B’ = (-1, 5)
- C’ = (-2, 9)
All side lengths and angles are unchanged.
What stays the same?
Size, shape, and orientation. Corresponding sides are parallel and equal in length. The shape is congruent to the original.
How do you find the rule from two points?
If P(7, -3) moves to P'(2, 1), then the shift is 2 – 7 = -5 in x and 1 – (-3) = 4 in y. The rule is (x – 5, y + 4).
What is a common mistake?
Applying the rule to only some vertices, or moving in the wrong direction on the y-axis.