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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 translation
rotation, then translation

translation, then rotation
translation, then rotation

rotation, then reflection
rotation, then reflection
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Answer 1

To determine the series of transformations that move the rectangle in Quadrant IV to the rectangle in Quadrant II, we can analyze the positions of the rectangles.

1. Reflection: First, the rectangle in Quadrant IV needs to be reflected across the y-axis. This reflection will reposition the rectangle such that its vertices will have their x-coordinates negated, moving them from Quadrant IV to Quadrant II.

2. Translation: After the reflection, the rectangle may need to be translated vertically to align properly with the rectangle in Quadrant II. In this case, the reflection alone places the rectangle in the correct quadrant, but depending on the alignment of the specific vertices, a translation might be necessary.

Thus, the correct series of transformations that occurs to move the rectangle from Quadrant IV to Quadrant II is:

Reflection, then translation.