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!