Question

Graph the triangle ABC after a 90 clockwise rotation around the center at origin.
a=(4,-3)
b=(4,0)
c=(8,0)

Answer 1

To perform a 90-degree clockwise rotation of the triangle ABC around the origin, we can use the rotation transformation for each point.

The general formula for a 90-degree clockwise rotation around the origin is:
\[
(x, y) \rightarrow (y, -x)
\]

Let's apply this transformation to each vertex of triangle ABC:

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

2. **Point B (4, 0)**:
\[
B' = (0, -4)
\]

3. **Point C (8, 0)**:
\[
C' = (0, -8)
\]

Now we have the new coordinates of the triangle after the rotation:
- \( A' = (-3, -4) \)
- \( B' = (0, -4) \)
- \( C' = (0, -8) \)

### Graphing the Triangle

1. Plot the points:
- Point A' at (-3, -4)
- Point B' at (0, -4)
- Point C' at (0, -8)

2. Connect the points A', B', and C' to form the triangle after the rotation.

Here is a simplified description of the triangle in relation to the graph:
- A' is located to the left of B' and below the x-axis.
- B' is directly on the line \(y = -4\).
- C' is below both A' and B' at \(y = -8\).

This forms the new triangle A'B'C' after the 90-degree clockwise rotation around the origin.