Question

Select the sequence of transformations that will carry rectangle A onto rectangle A'. A) reflect over y-axis, rotate 90° clockwise, then reflect over x-axis B) rotate 180° clockwise, reflect over y-axis, then translate 3 units left C) rotate 180° clockwise, reflect over x-axis, then translate 2 units left D) rotate 90° clockwise, reflect over y axis, then translate 3 units left

Answer 1

The student's query pertains to finding the correct sequence of geometric transformations—that is, reflections, rotations, and translations—that will map rectangle A onto rectangle A'.

Step-by-step explanation:

The student's question involves determining the sequence of geometric transformations that map one figure (rectangle A) onto another (rectangle A'). The answer would depend on the initial and final positions of the rectangles, which are not given here. However, a general approach to solving such a problem includes applying a combination of reflections, rotations, and translations over the coordinate axes. In this context, the question provides four different sequences of transformations that must be evaluated based on the positions of A and A'.

For example, a reflection over the y-axis will change the sign of the x-coordinates of the rectangle's vertices, while preserving the y-coordinates. A rotation of 90° clockwise around the origin would essentially switch the coordinates of each point (with some changes in sign), and a translation would shift all points of the rectangle in a specific direction (vertically upward/downward or horizontally to the left/right) within the coordinate system. The chosen sequence must result in rectangle A coinciding with rectangle A' after all the transformations are applied.