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Question

A coordinate plane with 4 quadrants shows x and y axes ranging from negative 8 to 8 in increments of 1. Three rectangles are formed by lines joining four plotted points each. Two of the rectangles are joined by rays connecting complementary vertices. The coordinates of the plotted points for the rectangle in quadrant 4 are left parenthesis 1 comma negative 3 right parenthesis, left parenthesis 1 comma negative 7 right parenthesis, left parenthesis 4 comma negative 7 right parenthesis, and left parenthesis 4 comma negative 3 right parenthesis. The coordinates for the rectangle in quadrant 2 are left parenthesis negative 2 comma 1 right parenthesis, left parenthesis negative 6 comma 1 right parenthesis, left parenthesis negative 6 comma 4 right parenthesis, and left parenthesis negative 2 comma 4 right parenthesis. The coordinates of the plotted points for the rectangle in quadrant 3 are left parenthesis negative 3 comma negative 1 right parenthesis, left parenthesis negative 7 comma negative 1 right parenthesis, left parenthesis negative 7 comma negative 4 right parenthesis, and left parenthesis negative 3 comma negative 4 right parenthesis. Four rays from each vertex of the rectangle in quadrant 3 connect to the complementary vertices of the rectangle in quadrant 2. A ray connects the point left parenthesis negative 7 comma negative 4 right parenthesis to left parenthesis negative 6 comma 1 right parenthesis. A ray connects the point left parenthesis negative 7 comma negative 1 right parenthesis to left parenthesis negative 6 comma 4 right parenthesis. A ray connects the point left parenthesis negative 3 comma negative 4 right parenthesis to left parenthesis negative 2 comma 1 right parenthesis. A ray connects the point left parenthesis negative 3 comma negative 1 right parenthesis to left parenthesis negative 2 comma 4 right parenthesis. The arrow heads are on the vertices of the rectangle in quadrant 2.
How would you describe the series of transformations that have occurred to move the rectangle in Quadrant IV to the rectangle in Quadrant II to show that the rectangles are congruent?(1 point)
Responses

reflection, then translation
reflection, then translation

rotation, then reflection
rotation, then reflection

rotation, then translation
rotation, then translation

translation, then rotation

Answer 1

To analyze the relationship between the rectangle in Quadrant IV and the rectangle in Quadrant II, we need to consider the transformations needed to move from one rectangle to the other, while preserving their congruence.

1. Reflection: The rectangle in Quadrant IV (with coordinates) is reflected over the y-axis to map it into Quadrant II. This reflection flips the rectangle across the y-axis, changing the signs of the x-coordinates of the rectangle in Quadrant IV.

2. Translation: After reflection, we may need to translate the rectangle vertically to align it properly if the y-coordinates differ significantly, due to the initial position of the rectangles.

Since the transformation begins with a reflection about the y-axis followed by a vertical translation to align the rectangles correctly, the series of transformations can be summarized as:

Reflection, then translation.

So the correct response is:

reflection, then translation.