The image you uploaded shows a coordinate plane with a rectangle whose vertices are labeled $D$, $E$, $F$, and $G$. You are asked to determine the coordinates of these points after a 90° counterclockwise rotation about the origin.

Rotation Rule for 90° Counterclockwise:

For a point $(x, y)$, the coordinates after a 90° counterclockwise rotation around the origin become: $(x', y') = (-y, x)$

Now, let’s apply this rule to each vertex:

1. Point $D$:

   • Original coordinates: $(-7, 1)$
   • After rotation: $(-1, -7)$

2. Point $E$:

   • Original coordinates: $(-7, 6)$
   • After rotation: $(-6, -7)$

3. Point $F$:

   • Original coordinates: $(-3, 6)$
   • After rotation: $(-6, -3)$

4. Point $G$:

   • Original coordinates: $(-3, 1)$
   • After rotation: $(-1, -3)$

Coordinates after 90° counterclockwise rotation:

• $D' = (-1, -7)$
• $E' = (-6, -7)$
• $F' = (-6, -3)$
• $G' = (-1, -3)$

Would you like further clarification or details on how this transformation works?

Here are some related questions to deepen your understanding:

1. How would you rotate a point 180° about the origin?
2. What changes when you rotate a point 90° clockwise instead of counterclockwise?
3. How would the coordinates change if the rotation was 270° counterclockwise?
4. Can you describe how to reflect a point across the y-axis?
5. How would you perform a translation instead of a rotation for these points?

Tip: For geometric transformations, visualizing the grid and tracing points can help confirm your answers.