To determine the sequence of reflections that transform quadrilateral ABCD into quadrilateral EFGH, we need to understand how reflections across the axes and the line y = x impact the coordinates of the points in the quadrilateral.
-
Reflecting over the line x = 0 (the y-axis): This will change the sign of the x-coordinates of all points. For a point (x, y), it moves to (-x, y).
-
Reflecting over the line y = 0 (the x-axis): This will change the sign of the y-coordinates of all points. For a point (x, y), it moves to (x, -y).
-
Reflecting over the line y = x: This swaps the x and y coordinates of all points. For a point (x, y), it moves to (y, x).
Now, let's analyze the steps based on the responses provided:
-
First response: Reflect over x = 0, then y = 0. This would reflect ABCD into the left side, and then flip it downward.
-
Second response: Reflect over y = x. This would swap the x and y coordinates, transforming the shape without flipping it over the axes.
-
Third response: Reflect first over y = 0, then over y = x. This would first flip the shape downwards and then swap coordinates, likely ending up in the second quadrant.
-
Fourth response: Reflect first over x = 0, then over y = x. This would flip the figure to the left, and then swap coordinates, which may also land it in the fourth quadrant.
To find the correct sequence, we need to identify the exact transformations that lead from ABCD in the second quadrant to EFGH in the fourth quadrant. Typically, reflecting across both axes toggles the sign of the coordinates and effectively moves the shape into another quadrant.
Therefore, the best fitting transformation from ABCD to EFGH would be:
Reflect ABCD first over the line x = 0, then over the line y = 0.
This implies flipping the figure to the left (placing it in the negative x region) and then flipping it downward, which should align it with the location of EFGH in the fourth quadrant.
1 answer