The question in the image is about a translation transformation $T_1$. The transformation moves point $(-3,6)$ to point $(5,-8)$. We are asked to determine where point $(2,-5)$ will move under the same transformation.

Step 1: Determine the translation vector

To find the translation vector, we subtract the coordinates of the initial point $(-3,6)$ from the coordinates of the final point $(5,-8)$:

$\text{Translation vector} = (5, -8) - (-3, 6) = (5 + 3, -8 - 6) = (8, -14)$

Thus, the translation vector is $(8, -14)$.

Step 2: Apply the translation to point $(2, -5)$

Now, apply the same translation vector $(8, -14)$ to the point $(2, -5)$:

$(2, -5) + (8, -14) = (2 + 8, -5 - 14) = (10, -19)$

Thus, under the same transformation, the point $(2,-5)$ will be translated to the point $(10, -19)$.

Final Answer:

The point $(2, -5)$ will move to $(10, -19)$.

Do you want more details or have any questions?

Here are five related questions to extend the topic:

1. What is the general formula for translating a point by a vector?
2. How would you describe a reflection transformation in comparison to translation?
3. Can you explain how to find the inverse of a translation transformation?
4. How does translation affect the distance between two points?
5. What are the properties of translations in the coordinate plane?

Tip: Translation always preserves the orientation and size of a geometric figure—it only shifts the figure by a certain amount.