Graph the triangle ABC after a 90 clockwise rotation around the center at origin.

Question

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.