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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

translation, then rotation
translation, then rotation

rotation, then translation
rotation, then translation

Answer 1

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

1. The rectangle in Quadrant IV has points with positive x-coordinates and negative y-coordinates, while the rectangle in Quadrant II has negative x-coordinates and positive y-coordinates.
2. To go from the rectangle in Quadrant IV to the rectangle in Quadrant II, we first need to reflect the rectangle across the y-axis. This is because the x-coordinates of the points change from positive to negative.
3. After the reflection across the y-axis, the rectangle will still be located in Quadrant IV, but now the y-coordinates will remain negative, corresponding to the original coordinates of Rectangle II, but flipped over the y-axis.
4. Finally, we need to translate the rectangle upwards (along the positive y-axis) so that the negative y-coordinates of Rectangle IV reach the corresponding positive y-coordinates of Rectangle II.

Thus, the transformations that occur are a reflection across the y-axis followed by a translation upwards.

The correct response is reflection, then translation.