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.