To rotate triangle $ABC$ with vertices $A(2,-1)$, $B(4,1)$, and $C(3,3)$ 90 degrees clockwise around the origin, we apply the following transformation:

$(x, y) \rightarrow (y, -x)$

Applying this transformation to each vertex:

• For $A(2,-1)$:
  $(2,-1) \rightarrow (-1,-2)$ So, $A'(-1,-2)$.

• For $B(4,1)$:
  $(4,1) \rightarrow (1,-4)$ So, $B'(1,-4)$.

• For $C(3,3)$:
  $(3,3) \rightarrow (3,-3)$ So, $C'(3,-3)$.

Therefore, the points of the image are:

$A'(-1,-2),B'(1,-4),C'(3,-3)$

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you rotate the triangle 90 degrees counterclockwise?
2. What are the coordinates if you rotate the triangle 180 degrees around the origin?
3. How does the area of the triangle change after rotation?
4. What would be the image if you rotate triangle $ABC$ around a different point?
5. How do the distances between the original and rotated vertices compare?

Tip: When rotating points on a coordinate plane, remember that a 90-degree clockwise rotation switches the coordinates and changes the sign of the original x-coordinate.