https://file.aiquickdraw.com/mathbot/file/1727373125390rs96kqjg.jpg

To perform a rotation of quadrilateral **SORT** by 270° counterclockwise about the origin, we need to use the transformation rules for rotating points around the origin.

For a 270° counterclockwise rotation about the origin, the rule for rotating a point \((x, y)\) is to transform it to \((y, -x)\).

Let's apply this transformation to each point of quadrilateral SORT:

1. **S(7, -6)** becomes **S'( -6, -7)**
2. **O(-2, -1)** becomes **O'( -1, 2)**
3. **R(-2, 3)** becomes **R'( 3, 2)**
4. **T(7, -2)** becomes **T'( -2, -7)**

### New Coordinates after 270° rotation:
- **S'(-6, -7)**
- **O'(-1, 2)**
- **R'(3, 2)**
- **T'(-2, -7)**

You can now plot these points on a coordinate plane to get the rotated image of quadrilateral SORT.

Would you like a detailed step-by-step explanation on how to plot this or how the transformation works? 

Here are some related questions:

1. What is the rule for rotating a figure 90° counterclockwise?
2. How do different rotations (90°, 180°, 270°) affect a figure's orientation?
3. How can you identify the center of rotation for any geometric transformation?
4. What would happen if we rotated the same figure by 360°?
5. How can we combine different transformations (e.g., rotation and reflection)?

**Tip**: Always make sure to label the new vertices clearly after performing transformations to keep track of each point's movement!

Draw the image of the rotation of quadrilateral SORT by 270° about the origin, where the coordinates of S(7,-6), O(-2,-1), R(-2,3), T(7,-2).

Learn how to rotate quadrilateral SORT by 270° counterclockwise about the origin. Using key geometric concepts such as the rotation transformation formula, this problem provides a detailed solution for rotating points on a coordinate plane. Suitable for students in Grades 8-10.

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