Answer:
The coordinates of the vertices of the triangle ABC after a rotation of 180 degrees about the origin are:
A'(-2,0), B'(1,-5), and C'(-4,-3).
Explanation:
To determine the coordinates of the vertices of the triangle ABC after a rotation of 180 degrees about the origin, we can use the following transformation rules:
For a rotation of 180 degrees about the origin:
- The x-coordinate becomes its negative counterpart.
- The y-coordinate becomes its negative counterpart.
Let's apply these rules to each vertex of the triangle:
Vertex A(2,0):
- The x-coordinate becomes -2.
- The y-coordinate remains 0.
Therefore, after the rotation, vertex A becomes A'(-2,0).
Vertex B(-1,5):
- The x-coordinate becomes 1.
- The y-coordinate becomes -5.
Therefore, after the rotation, vertex B becomes B'(1,-5).
Vertex C(4,3):
- The x-coordinate becomes -4.
- The y-coordinate becomes -3.
Therefore, after the rotation, vertex C becomes C'(-4,-3).