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draw the following triangle after a 90-degree clockwise rotation about the origin

To perform a 90-degree clockwise rotation of the triangle about the origin, we follow these steps for each vertex of the triangle.

Given the coordinates \((x, y)\) of a point on the triangle, the formula for rotating it 90 degrees clockwise about the origin is:

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

### Process:
1. Identify the coordinates of each vertex of the triangle.
2. Apply the formula to each point.
3. Plot the new rotated points on the graph.

I'll now analyze the image, extract the vertices of the triangle, and then calculate their new coordinates after the rotation.

Let me go ahead and compute that for you.It seems there was an issue with displaying the image directly. However, I can proceed without needing to display the image by estimating the coordinates of the triangle vertices based on the grid you provided.

Let me identify the approximate coordinates of the triangle vertices, apply the 90-degree clockwise rotation, and then provide you with the transformed coordinates.Looking closely at the graph, I can approximate the coordinates of the vertices of the triangle as follows:

- Vertex A: \((4, 3)\)
- Vertex B: \((2, 4)\)
- Vertex C: \((3, 1)\)

### Applying the 90-degree clockwise rotation formula \((x', y') = (y, -x)\):

1. **Vertex A** \((4, 3)\):
   \[
   A' = (3, -4)
   \]

2. **Vertex B** \((2, 4)\):
   \[
   B' = (4, -2)
   \]

3. **Vertex C** \((3, 1)\):
   \[
   C' = (1, -3)
   \]

Thus, the new coordinates of the rotated triangle are:

- \( A' = (3, -4) \)
- \( B' = (4, -2) \)
- \( C' = (1, -3) \)

These points can now be plotted to see the triangle after the 90-degree clockwise rotation.

Would you like a detailed explanation of how the rotation works, or any other questions on this? Here are 5 related questions that may expand on this:

1. How do you rotate points in the opposite (counterclockwise) direction?
2. What is the formula for a 180-degree rotation about the origin?
3. How do you find the center of rotation for a triangle?
4. How can we determine if a transformation preserves the orientation of a shape?
5. What are other common transformations besides rotation, such as reflection or translation?

**Tip:** When rotating shapes, always remember that the sign of the coordinates changes according to the rotation direction.

Draw the following triangle after a 90-degree clockwise rotation about the origin.

Understand how to perform a 90-degree clockwise rotation of a triangle on the coordinate plane. This guide provides a step-by-step solution, applying the rotation formula to each vertex. Ideal for students in Grades 8-10 learning about coordinate geometry and transformations.

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