To determine which rule yields a similar figure instead of a congruent figure, let's analyze the options:
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Option #1: (x,y)→(x+h,y+k) - This represents a translation, which moves the figure but maintains its size and shape, resulting in a congruent figure.
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Option #2: (x,y)→(kx,ky) - This represents a dilation if \( k \) is not equal to 1. If \( k \) is greater than 1, the figure will enlarge; if \( k \) is between 0 and 1, the figure will reduce in size. This transformation yields a similar figure but not congruent.
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Option #3: (x,y)→(−x,−y) - This is a reflection through the origin, which results in a congruent figure since the size and shape remain the same.
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Option #4: (x,y)→(y,x) - This represents a reflection over the line \( y = x \), which keeps the size and shape the same, thus yielding a congruent figure.
Based on the analysis, the correct answer is:
Option #2: (x,y)→(kx,ky).
This rule yields a similar figure, depending on the value of \( k \).
1 answer