Question

The triangle below is rotated 270° counterclockwise.



What are the new coordinates of the vertices of the triangle?
A.(-1, 3), (-6, 3), (-6, 8)
B.(3, 1), (3, 6), (8, 6)
C.(3, -1), (3, -6), (8, -6)
D.(-3, -1), (-3, -6), (-8, -6)

Answer 1

To find the new coordinates of the triangle's vertices after a 270° counterclockwise rotation about the origin, we can use the transformation rule for rotating a point (x, y) by 270° counterclockwise which is:

\[
(x, y) \rightarrow (y, -x)
\]

Let's assume the original coordinates of the vertices of the triangle are given. However, since the original coordinates of the triangle vertices are not provided in your question, I'll illustrate the rotation using a generic point (x, y) and then check if any of the options correspond to this transformation.

1. **Transform the vertex (x, y)**:

Using the transformation:
\[
(x, y) \rightarrow (y, -x)
\]

This means:
- The x-coordinate becomes the original y-coordinate.
- The y-coordinate becomes the negative of the original x-coordinate.

2. **Apply the transformation to all vertices**

Let’s apply this to three vertices of a triangle. If we have vertices (x1, y1), (x2, y2), and (x3, y3), their new coordinates after a 270° rotation counterclockwise will be:
- Vertex 1: (y1, -x1)
- Vertex 2: (y2, -x2)
- Vertex 3: (y3, -x3)

3. **Checking options**:

We do not have the original vertices, but we'll evaluate the provided options to see if any of them could represent the transformation outcome based on typical coordinates. Unfortunately, without the original coordinates of the triangle, we can't directly choose any option.

However, if you provide the original triangle vertices, I would calculate and identify the correct answer among the options.