To determine the new coordinates of triangle $\triangle GEF$ after a 270° clockwise rotation about the origin, follow the rotation rule:

Rotation Rule (270° Clockwise):

If a point $(x, y)$ is rotated 270° clockwise, its new coordinates will be: $(x, y) \rightarrow (y, -x)$

Step 1: Identify Original Coordinates

From the graph:

• $G(-4, 1)$
• $E(-2, -2)$
• $F(-4, -3)$

Step 2: Apply the Rotation Rule

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

1. For $G(-4, 1)$: $(-4, 1) \rightarrow (1, 4)$
2. For $E(-2, -2)$: $(-2, -2) \rightarrow (-2, 2)$
3. For $F(-4, -3)$: $(-4, -3) \rightarrow (-3, 4)$

Step 3: New Coordinates

The new coordinates are:

• $G'(1, 4)$
• $E'(-2, 2)$
• $F'(-3, 4)$

Compare to Answer Choices

From the options:

• Correct coordinates are missing from the listed options, suggesting a discrepancy or omission in the answer choices.

Let me know if you need clarification or further breakdown! Here are five related questions to deepen understanding:

1. How do you rotate a point $(x, y)$ 90° clockwise around the origin?
2. What happens when you rotate a point 180° about the origin?
3. Can you explain the difference between clockwise and counterclockwise rotations?
4. How do transformations (e.g., translations, rotations) affect a shape's size and orientation?
5. How do you verify graphically that a rotation is accurate?

Tip: For a 270° clockwise rotation, the coordinates $(x, y)$ always map to $(y, -x)$.