vertices of triangle ABC are A(2,-2), B(-3,-2), and C(-1,3). what are the cpordinates of vertices of triangle A’B’C’ for the rotation. r (270^degree, o)


To perform a 270° counterclockwise rotation about the origin, we can apply the following transformation to each point \((x, y)\):

\[
(x', y') = (y, -x)
\]

### Applying this to each vertex:

1. **Point A (2, -2):**
   \[
   A' = (-2, -2)
   \]
   
2. **Point B (-3, -2):**
   \[
   B' = (-2, 3)
   \]
   
3. **Point C (-1, 3):**
   \[
   C' = (3, 1)
   \]

### The coordinates of the vertices of triangle \(A'B'C'\) after a 270° counterclockwise rotation are:

\[
A'(-2, -2), B'(-2, 3), C'(3, 1)
\]

Let me know if you want more details or if you have any further questions.

Here are 5 related questions to deepen your understanding:

1. What would the coordinates be for a 90° counterclockwise rotation of the same triangle?
2. How do you calculate the area of triangle ABC using its vertices?
3. What are the rules for rotating a point by 180° about the origin?
4. Can you derive the formula for rotating a point by any arbitrary angle?
5. What are the reflection coordinates of the triangle over the x-axis?

**Tip:** When performing transformations, it's helpful to first visualize the triangle and confirm the new coordinates to ensure accuracy.

Vertices of triangle ABC are A(2,-2), B(-3,-2), and C(-1,3). What are the coordinates of vertices of triangle A’B’C’ for the rotation r(270°, O)?

Learn how to find the new coordinates of triangle ABC after a 270-degree counterclockwise rotation around the origin. This geometry problem involves applying rotation transformations in coordinate geometry and is suitable for students in Grades 9-12.

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