Write a rule to translate  $\triangle P'$ $Q'$ $R'$  to $△PQR$ .




To translate $ \triangle P'Q'R' $ to $ \triangle PQR $, you need to apply the same translation to each of the corresponding points $ P', Q', R' $ to map them to $ P, Q, R $ respectively. The rule for translation is given by a vector that defines how each point moves from the transformed triangle to the original triangle.

Let the translation vector be $ \vec{v} = (a, b) $, where $ a $ is the horizontal shift and $ b $ is the vertical shift. Then, the rule for translating $ \triangle P'Q'R' $ to $ \triangle PQR $ is:

\[
(x', y') \to (x, y) \quad \text{where} \quad (x, y) = (x' + a, y' + b)
\]

- $ P' \to P: P(x', y') = P(x'+a, y'+b) $
- $ Q' \to Q: Q(x', y') = Q(x'+a, y'+b) $
- $ R' \to R: R(x', y') = R(x'+a, y'+b) $

To find the values of $ a $ and $ b $, simply subtract the coordinates of $ P' $ from $ P $, or $ Q' $ from $ Q $, or $ R' $ from $ R $, since all points are translated by the same vector.

### Example:
If $ P'(x_1', y_1'), Q'(x_2', y_2'), R'(x_3', y_3') $ and $ P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3) $, then:
\[
a = x_1 - x_1', \quad b = y_1 - y_1'
\]

Apply this vector $ (a, b) $ to translate the other points $ Q' $ and $ R' $ as well.

Would you like further details or examples?

Here are 5 relative questions:
1. How do you calculate the translation vector if given both triangles?
2. How does the translation differ from a reflection or rotation?
3. Can a translation change the size or shape of a triangle?
4. What is the importance of preserving congruency in translation?
5. How can you apply this translation rule to polygons beyond triangles?

**Tip**: Always verify the vector by checking all corresponding vertices of both triangles!

Write a rule to translate  $\triangle P'Q'R'$ to $\triangle PQR$.

Learn how to translate a triangle $\triangle P'Q'R'$ to $\triangle PQR$ using a vector. This guide includes a step-by-step solution, translation rule formula, and example. Ideal for students in Grades 8-10 studying translations in geometry.

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