Question

Consider figures 1 and 2 shown on the coordinate plane. Figure 1 has been transformed to produce figure 2. Graph shows 2 quadrilaterals plotted on a coordinate plane. Quadrilateral 1 in quadrant 1 has vertices at (1, 3), (2, 5), (5, 5), (5, 3). Quadrilateral 2 in quadrant 4 has vertices at (1, minus 3), (5, minus 3), (5, minus 5), (2, minus 5). Describe the transformation. This transformation can be described by?

Answer 1

The transformation from Quadrilateral 1 to Quadrilateral 2 is a reflection over the x-axis, where the y-coordinates of the vertices of the original figure have been inverted.

Step-by-step explanation:

Reflecting the coordinates of the given vertices of Quadrilateral 1, we can see that each vertex (x, y) has been transformed to (x, -y). Specifically, the point (1, 3) became (1, -3), the point (2, 5) transformed to (2, -5), and similarly for the other vertices. This transformation is a reflection over the x-axis. In this case, the y-coordinates have been multiplied by -1, while the x-coordinates remain unchanged.

When transforming figures on the coordinate plane, a reflection is one such operation that flips a figure over a line, known as the axis of reflection. In our case, the axis of reflection is the x-axis. With reflections, the image maintains the same size and shape as the original figure, but the orientation is reversed as if looking in a mirror placed along the axis of reflection.