https://file.aiquickdraw.com/mathbot/file/1726781602784m5ar5eif.jpg

T is at (5,-5) U is at (15,-5) and V is at (5,-20)

To rotate triangle \( \triangle TUV \) 90° clockwise around the origin, we apply the standard 90° clockwise rotation formula. For each point \( (x, y) \), the new coordinates after a 90° clockwise rotation around the origin are given by:

\[
(x', y') = (y, -x)
\]

Let's calculate the new coordinates for each vertex:

1. **Point \( T(5, -5) \):**
   \[
   T'(x', y') = (-5, -5)
   \]

2. **Point \( U(15, -5) \):**
   \[
   U'(x', y') = (-5, -15)
   \]

3. **Point \( V(5, -20) \):**
   \[
   V'(x', y') = (-20, -5)
   \]

So, after the 90° clockwise rotation, the new coordinates of the triangle \( \triangle TUV \) are:
- \( T'(-5, -5) \)
- \( U'(-5, -15) \)
- \( V'(-20, -5) \)

Would you like further details or a step-by-step explanation?

Here are some follow-up questions:
1. What is the formula for rotating a point counterclockwise instead?
2. How would the coordinates change if we rotated the triangle 180°?
3. What happens to the area of the triangle after a rotation?
4. Can you derive the transformation matrix for a 90° clockwise rotation?
5. What is the effect of rotating the triangle by 270° clockwise?

**Tip:** For rotations around a point other than the origin, you need to first translate the shape to the origin, perform the rotation, and then translate it back.

Rotate △TUV 90° clockwise around the origin. The coordinates of the points are: T(5, -5), U(15, -5), and V(5, -20).

Learn how to rotate triangle △TUV 90° clockwise around the origin. The vertices T(5, -5), U(15, -5), and V(5, -20) transform based on the formula (x', y') = (y, -x) for 90° rotations. Suitable for Grades 8-10.

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