To determine which transformation will result in a rectangle that is not congruent to the original rectangle, we can analyze the effects of each transformation:
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Dilation by a scale factor of 3: This transformation changes the size of the rectangle, making it larger. The new rectangle will not be congruent to the original since congruence requires identical shapes and sizes.
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Rotation of 180 degrees counterclockwise: This transformation changes the orientation of the rectangle but does not alter its size or shape. Thus, it will be congruent to the original rectangle.
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Translation 90 units to the right: This transformation moves the rectangle but keeps its size and shape unchanged. Therefore, the resulting rectangle is congruent to the original.
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Reflection across the x-axis: This transformation flips the rectangle over the x-axis. Like rotation and translation, it does not change the size or shape, so the rectangle remains congruent to the original.
Based on the analysis above, the transformation that will result in a rectangle that is NOT congruent to the original rectangle is:
A dilation by a scale factor of 3.