To solve this problem, let’s walk through how to find the new coordinates after rotating the given points 270° counterclockwise about the origin.

Key Concept: Rotation by 270° Counterclockwise

• A 270° counterclockwise rotation transforms a point $(x, y)$ to $(y, -x)$.

Now, let's extract the vertices from the graph shown in your image:

1. Point R: $(-2, 3)$
2. Point S: $(-4, 1)$
3. Point T: $(-1, -1)$
4. Point U: $(-3, -4)$

Rotation Calculation: 270° Counterclockwise

Using the transformation rule $(x, y) \rightarrow (y, -x)$:

• R(-2, 3) → $(3, 2)$
• S(-4, 1) → $(1, 4)$
• T(-1, -1) → $(-1, 1)$
• U(-3, -4) → $(-4, 3)$

New Coordinates after 270° Counterclockwise Rotation

• R': $(3, 2)$
• S': $(1, 4)$
• T': $(-1, 1)$
• U': $(-4, 3)$

Let me know if you need more details or if anything is unclear!

5 Related Questions:

1. What is the general formula for 90° and 180° rotations?
2. How do clockwise and counterclockwise rotations differ?
3. How do rotations affect the orientation of a shape?
4. What are other transformations besides rotations (e.g., translations, reflections)?
5. How would the coordinates change if the rotation was around a different point instead of the origin?

Tip: For easier rotation of coordinates, remember that a 270° counterclockwise rotation is equivalent to a 90° clockwise rotation.