https://file.aiquickdraw.com/mathbot/file/1727267306650rev00epj.jpg

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.

Sebuah translasi T1 untuk memindahkan titik (-3,6) ke titik (5,-8), dengan translasi yang sama titik (2,-5) akan bergeser ke titik ...

Solve a translation problem where point (-3,6) is translated to (5,-8), and determine the new position of point (2,-5) under the same transformation. Learn how to calculate translation vectors in coordinate geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation