Question

Which rule will yield a similar figure instead of a congruent figure?Option #1: (x,y)→(x+h,y+k)Option #2: (x,y)→(kx,ky)Option #3: (x,y)→(−x,−y)Option #4: (x,y)→(y,x)(1 point)The correct response is Option #.Remaining Attempts : 1View previous attemptSkip to navigation

Answer 1

To determine which rule yields a similar figure instead of a congruent figure, let's analyze the options:

1. **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.

2. **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.

3. **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.

4. **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 \( k \).