To solve the problem of transforming the triangle $\triangle GHI$, we need to follow these steps:

Step 1: Perform a 180° rotation counterclockwise around the origin

The rule for rotating a point $(x, y)$ by 180° counterclockwise around the origin is:
$(x, y) \to (-x, -y)$

1. Let’s identify the coordinates of the vertices of $\triangle GHI$:

   • $G = (10, -12)$
   • $H = (7, -8)$
   • $I = (4, -12)$

2. Apply the 180° rotation to each vertex:

   • $G(10, -12) \to G'(-10, 12)$
   • $H(7, -8) \to H'(-7, 8)$
   • $I(4, -12) \to I'(-4, 12)$

Step 2: Translate 1 unit left and 21 units down

The rule for translating a point $(x, y)$ by $a$ units left and $b$ units down is:
$(x, y) \to (x - a, y - b)$ Here, $a = 1$ and $b = 21$.

1. Translate the rotated points $G', H', I'$:
   • $G'(-10, 12) \to G''(-10 - 1, 12 - 21) = (-11, -9)$
   • $H'(-7, 8) \to H''(-7 - 1, 8 - 21) = (-8, -13)$
   • $I'(-4, 12) \to I''(-4 - 1, 12 - 21) = (-5, -9)$

Step 3: Graph the transformed triangle $G''H''I''$

The final coordinates are:

• $G'' = (-11, -9)$
• $H'' = (-8, -13)$
• $I'' = (-5, -9)$

You can now plot these points on the graph to display the transformed triangle.

Let me know if you need a visual sketch or further clarification!

Related Questions

1. How do you perform rotations for other angles like 90° or 270°?
2. What happens to a point when you reflect it over the x-axis or y-axis?
3. Can you explain how translations affect the position of a shape?
4. How can you determine if two shapes are congruent after transformations?
5. What is the general rule for combining multiple transformations?

Tip: Always perform rotations before translations for clarity when combining transformations.