To rotate the quadrilateral $SORT$ by $270^\circ$ counterclockwise about the origin, we follow these steps for each vertex of the quadrilateral. The formula for rotating a point $(x, y)$ by $270^\circ$ counterclockwise around the origin is:

$(x', y') = (y, -x)$

Here are the steps for each point in quadrilateral $SORT$:

1. Point $S(-2, -2)$: After rotation by $270^\circ$: $S' = (-2, -(-2)) = (-2, 2)$

2. Point $O(-2, 1)$: After rotation by $270^\circ$: $O' = (1, 2)$

3. Point $R(1, 3)$: After rotation by $270^\circ$: $R' = (3, -1)$

4. Point $T(5, 1)$: After rotation by $270^\circ$: $T' = (1, -5)$

Now that we have the coordinates of the rotated points, you can plot them on the grid to complete the quadrilateral. The new coordinates of the rotated quadrilateral $S' O' R' T'$ are:

$S'(-2, 2), O'(1, 2), R'(3, -1), T'(1, -5)$

Would you like further assistance with plotting or visualizing this rotation?

Here are five related questions to consider:

1. How do you rotate a point by $90^\circ$ about the origin?
2. What is the effect of rotating a shape by $180^\circ$ around the origin?
3. What happens to the coordinates if you rotate by $360^\circ$?
4. How does rotating by $270^\circ$ differ from rotating by $-90^\circ$?
5. How would the shape look if rotated by only $90^\circ$?

Tip: When rotating shapes, always check the signs of the new coordinates to ensure the correct quadrant placement.