https://file.aiquickdraw.com/mathbot/file/1728400065356o288prdj.jpg

The expression in the image shows a translation of the point \((5,9)\) by the vector \(\langle -8,2 \rangle\). A translation moves a point by adding the vector's components to the point's coordinates.

In this case, we have:

\[
T_{\langle -8, 2 \rangle}(5, 9)
\]

To perform the translation:
- For the x-coordinate: \( 5 + (-8) = 5 - 8 = -3 \)
- For the y-coordinate: \( 9 + 2 = 11 \)

Thus, the translated point is:

\[
(-3, 11)
\]

Do you want more details, or have any questions?

Here are five related questions:
1. What is the general formula for translating a point by a vector?
2. How does translation differ from rotation in transformations?
3. Can you describe the result of translating a point by the vector \(\langle a, b \rangle\)?
4. How would the point \((x, y)\) be affected by translating with a negative vector?
5. How are translations applied to geometric shapes?

**Tip:** When translating points, remember to always add the vector components directly to the point's coordinates!

Translate the point (5, 9) by the vector ⟨-8, 2⟩.

Learn how to translate the point (5,9) by the vector ⟨-8,2⟩ with a detailed explanation of how vector addition works in coordinate geometry. This exercise covers key concepts of translation and vector addition, ideal for students in Grades 7-9.

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