a pentagon with vertices at (1,1),(2,3),(4,3),(5,1),&(3,0) is transformed to a pentagon with vertices at (1,-1),(2,-3),(4,-3),(5,-1),&(3,0) which is transformation was applied?

Question

A. rotation 180 degrees about the origin
B. rotation 90 degrees counterclockwise about the origin
C. translation 2 units down
D. reflection over the x-axis

Answer 1

To determine which transformation was applied to the original pentagon with vertices at \((1,1)\), \((2,3)\), \((4,3)\), \((5,1)\), and \((3,0)\) to obtain the transformed pentagon with vertices at \((1,-1)\), \((2,-3)\), \((4,-3)\), \((5,-1)\), and \((3,0)\), we can analyze the changes in the coordinates of the vertices.

Let's compare the original vertices with the transformed vertices:

1. Vertex (1, 1) transforms to \((1, -1)\)
2. Vertex (2, 3) transforms to \((2, -3)\)
3. Vertex (4, 3) transforms to \((4, -3)\)
4. Vertex (5, 1) transforms to \((5, -1)\)
5. Vertex (3, 0) stays the same at \((3, 0)\)

Notice that the y-coordinates of the first four vertices are negated (the value of y is multiplied by -1), while the x-coordinates remain unchanged for all vertices. This indicates that the transformation involved reflects the points across the x-axis.

Thus, the correct answer is:

D. reflection over the x-axis.