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The problem describes a transformation of triangle \(ABC\) through two steps: a translation followed by a rotation. Let's break down the steps systematically.

### Given:
- \( A(-1, 3), B(5, -3), C(2, 4) \)
- Translation by \( T\left(-3, -2\right) \)
- Rotation of 90° clockwise about the origin.

### Step 1: Translation
To apply the translation \(T(-3, -2)\), we add \((-3, -2)\) to each point.

For point \( A(-1, 3) \):
\[
A' = (-1 + (-3), 3 + (-2)) = (-4, 1)
\]

For point \( B(5, -3) \):
\[
B' = (5 + (-3), -3 + (-2)) = (2, -5)
\]

For point \( C(2, 4) \):
\[
C' = (2 + (-3), 4 + (-2)) = (-1, 2)
\]

### Step 2: Rotation by 90° Clockwise
To rotate a point \((x, y)\) by 90° clockwise around the origin, the formula is:
\[
(x', y') = (y, -x)
\]

Applying this to the translated points:

For \( A'(-4, 1) \):
\[
A'' = (1, 4)
\]

For \( B'(2, -5) \):
\[
B'' = (-5, -2)
\]

For \( C'(-1, 2) \):
\[
C'' = (2, 1)
\]

### Final coordinates:
- \(A''(1, 4)\)
- \(B''(-5, -2)\)
- \(C''(2, 1)\)

Thus, the correct answer is **D**: \( A''(1,4), B''(-5,-2), C''(2,1) \).

Would you like further details on any of the steps? Here are 5 related questions for deeper understanding:

1. How would the transformation change if the rotation was counterclockwise?
2. What is the general formula for a 90° clockwise rotation around any point other than the origin?
3. Can you calculate the distance between the original and translated points?
4. How does a reflection differ from a rotation in terms of transformation?
5. What is the composition of multiple transformations in geometry?

**Tip**: When rotating points, always visualize or draw the axes to avoid mistakes!

Diketahui segitiga ABC dengan titik A(-1, 3), B(5, -3), dan C(2, 4) ditranslasi oleh T(-3, -2), kemudian dilanjutkan rotasi sejauh 90° searah jarum jam. Bayangan ketiga titik tersebut adalah ...

This problem involves translating triangle ABC with vertices at A(-1,3), B(5,-3), and C(2,4) by T(-3,-2), followed by a 90° clockwise rotation. Learn how to apply these transformations and calculate the final coordinates. Ideal for students in Grades 10-12.

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