Question

The vertices of a rectangle are F(-5, -1), G(-2, -1), H(-2, -3), and I(-5, -3).

Rotate the rectangle 270° clockwise about the origin, and then reflect it in the
y-axis. What are the coordinates of the image?

Answer 1

To transform the rectangle, we rotate it 270° clockwise and reflect it in the y-axis, resulting in the final image coordinates F'(1, 5), G'(1, 2), H'(3, 2), and I'(3, 5).

Step-by-step explanation:

The student is asking about a transformation in which a rectangle with given vertices is first rotated 270° clockwise around the origin and then reflected in the y-axis. To find the coordinates of the image post-transformation, we will perform these operations step-by-step:

1. For a 270° clockwise rotation about the origin, the coordinates (x, y) transform into (y, -x). Thus, the image after rotation will have vertices F'(-1, 5), G'(-1, 2), H'(-3, 2), and I'(-3, 5).
2. The reflection in the y-axis transforms the coordinates (x, y) into (-x, y). Applying this to the rotated vertices, we get F'(1, 5), G'(1, 2), H'(3, 2), and I'(3, 5) as the final coordinates of the image.