The image contains two geometry tasks involving transformations on the coordinate plane. Here's how to solve each part:

Task 4:

• Vertices of Triangle ABC:

  • $A(3,3)$
  • $B(1,3)$
  • $C(2,1)$

• Steps:

  1. Graph the Triangle ABC: Plot the points $A(3,3)$, $B(1,3)$, and $C(2,1)$ on the coordinate plane and connect them to form a triangle.
  2. Rotate 90 Degrees Clockwise About the Origin:
     • The rule for rotating a point 90° clockwise is: $(x, y) \to (y, -x)$
     • Applying the rule:
       • $A(3,3) \to A'(3,-3)$
       • $B(1,3) \to B'(3,-1)$
       • $C(2,1) \to C'(1,-2)$
  3. Graph the New Triangle $A'B'C'$: Plot $A'(3,-3)$, $B'(3,-1)$, and $C'(1,-2)$ and connect them.
  4. Write the Rule: The rule for this rotation is $(x, y) \to (y, -x)$.

Task 5:

• Vertices of Triangle ABC:

  • $A(-2,0)$
  • $B(0,3)$
  • $C(2,2)$

• Steps:

  1. Graph the Triangle ABC: Plot $A(-2,0)$, $B(0,3)$, and $C(2,2)$ on the coordinate plane and connect them to form a triangle.
  2. Reflect Over the y-Axis:
     • The rule for reflecting over the y-axis is: $(x, y) \to (-x, y)$
     • Applying the rule:
       • $A(-2,0) \to A'(2,0)$
       • $B(0,3) \to B'(0,3)$
       • $C(2,2) \to C'(-2,2)$
  3. Graph the New Triangle $A'B'C'$: Plot $A'(2,0)$, $B'(0,3)$, and $C'(-2,2)$ and connect them.
  4. Write the Rule: The rule for this reflection is $(x, y) \to (-x, y)$.

Would you like a detailed sketch or further explanation?

Questions to Expand Learning:

1. What happens if you rotate the triangles 90° counterclockwise instead?
2. How does reflecting over the x-axis change the triangle's coordinates?
3. Can you describe how a 180° rotation differs from a 90° rotation?
4. What would be the result of reflecting over the line $y = x$?
5. How can you verify the transformations mathematically without graphing?

Tip: Always double-check transformed coordinates by reapplying the transformation rule for accuracy.