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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

rotation, then reflection
rotation, then reflection

translation, then rotation
translation, then rotation
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Answer 1

To determine the series of transformations that have occurred to move the rectangle in Quadrant IV to the rectangle in Quadrant II, we can analyze the situation:

1. Reflection: The rectangle in Quadrant IV (with vertices at (1, -3), (1, -7), (4, -7), and (4, -3)) is located in the lower right region of the coordinate plane, while the rectangle in Quadrant II (with vertices at (-2, 1), (-6, 1), (-6, 4), and (-2, 4)) is located in the upper left region. To move from Quadrant IV to Quadrant II, a reflection over the y-axis (the line x = 0) would first be appropriate. This transformation reflects all points horizontally.

2. Translation: After reflecting the rectangle, the next step involves translating the reflected rectangle. This translation moves the rectangle upward to align it with the coordinates of the rectangle in Quadrant II.

Thus, the correct sequence to describe how the rectangle in Quadrant IV transforms into the rectangle in Quadrant II is:

Reflection, then translation.

So the correct response to the question is: reflection, then translation.