To determine the type of transformation shown in the image with polygons EFGH and E'F'G'H', you can analyze their positions relative to each other. Here are the characteristics of each type of transformation:
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Reflection across the x-axis: The points of the polygon will have their y-coordinates changed to their negatives. For example, a point (x, y) will become (x, -y).
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Horizontal translation: This shifts the entire polygon left or right without changing its orientation or shape.
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Vertical translation: This shifts the entire polygon up or down without changing its orientation or shape.
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180° clockwise rotation: This rotates the polygon around the center point. A point (x, y) will change to (-x, -y).
Given these descriptions, look at the arrangement of the two polygons. If the new polygon E'F'G'H' appears directly above or below EFGH, it is likely a vertical translation. If it appears directly to the right or left, it is a horizontal translation. If the y-coordinates are flipped while the x-coordinates remain the same, it is a reflection across the x-axis. If the corners of E'F'G'H' are the opposite side of EFGH, it indicates a 180° rotation.
Without the actual image, it's tough to conclude definitively, but use those guidelines to focus on how E'F'G'H' relates to EFGH.