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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

rotation, then translation
rotation, then translation

rotation, then reflection
rotation, then reflection

translation, then rotation
translation, then rotation

reflection, then translation

Answer 1

To move the rectangle in Quadrant IV to the rectangle in Quadrant II and show that they are congruent, we can analyze the positions of the rectangles.

1. Reflection: The rectangle in Quadrant IV can be reflected across the y-axis to move it into Quadrant III. This reflection changes the signs of the x-coordinates, effectively flipping the rectangle over the y-axis.

2. Translation: After reflection, we can translate the rectangle vertically upward to get it into Quadrant II.

This means the series of transformations is: reflection, then translation.

The correct response is: reflection, then translation.