Integrated Math 1 / Unit 8: Transformations and Congruence
8.2 Translations
Notes
A translation slides every point the same distance in the same direction.
- Rule: $(x, y) \to (x + a, y + b)$. Positive $a$ moves right; positive $b$ moves up.
- The image is the same shape, size and orientation as the preimage; segments stay parallel to their images.
- Example: $(x, y) \to (x + 4, y - 2)$ sends $(3, 5)$ to $(7, 3)$.
- To find the rule, subtract coordinates: image $-$ preimage.
Practice
The translation $(x, y) \to (x + 4, y - 2)$ is applied to $(3, 5)$. What is the image?
Add 4 to $x$: $3 + 4 = 7$. Subtract 2 from $y$: $5 - 2 = 3$.
Point $A(1, 2)$ is translated to $A'(-2, 6)$. What is the translation rule?
$x$ changes by $-2 - 1 = -3$ and $y$ changes by $6 - 2 = 4$.
Point $A(-3, 4)$ is translated to $A'(2, 4)$. Which describes the translation?
The $y$-coordinate does not change and $x$ increases by 5.
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