The problem involves rotating a shape on a coordinate grid. The specific task here is to rotate the given triangle 180° about the origin.

Step-by-Step Solution:

1. Understand the Transformation Rule:

   • A rotation of 180° about the origin transforms any point $(x, y)$ to $(-x, -y)$.

2. Identify the Vertices:

   • Locate the vertices of the triangle on the grid. From observation:
     • $J = (-3, -2)$
     • $H = (-5, -4)$
     • $O = (0, 0)$

3. Apply the Rotation Rule:

   • Transform each vertex using the rule:
     • For $J(-3, -2)$, the new coordinates are $J'(3, 2)$.
     • For $H(-5, -4)$, the new coordinates are $H'(5, 4)$.
     • For $O(0, 0)$, the new coordinates remain $O'(0, 0)$.

4. Plot the New Coordinates:

   • Mark the points $J'(3, 2)$, $H'(5, 4)$, and $O'(0, 0)$ on the grid.
   • Connect the points to form the rotated triangle.

Would you like me to redraw this on a grid or provide further explanations?

Related Questions:

1. What would the triangle look like after a 90° clockwise rotation around the origin?
2. How do the coordinates change when rotating by 270° about the origin?
3. What are the properties of rotations in the coordinate plane (e.g., isometry)?
4. How do you find the center of rotation if it's not at the origin?
5. What happens to a point on the x-axis when rotated 180°?

Tip:

When performing rotations, always double-check your transformation rules for clarity and accuracy!