Question

Which rule will yield a similar figure instead of a congruent figure?

Option #1: \((x,y)→(x+h,y+k)\)

Option #2: \((x,y)→\left(kx,ky\right)\)

Option #3: \((x,y)→(-x,-y)\)

Option #4: \((x,y)→(y,x)\)

(1 point)
The correct response is Option #
.

Answer 1

To determine which rule yields a similar figure instead of a congruent figure, we need to analyze each option:

1. **Option #1: \((x,y)→(x+h,y+k)\)** - This is a translation of the figure by \(h\) units in the x-direction and \(k\) units in the y-direction. This results in a congruent figure, as the shape and size remain the same.

2. **Option #2: \((x,y)→\left(kx,ky\right)\)** - This is a scaling transformation. Depending on the value of \(k\) (if \(k \neq 1\)), it will enlarge or shrink the figure while maintaining the shape. This results in a similar figure but not a congruent one.

3. **Option #3: \((x,y)→(-x,-y)\)** - This is a rotation by 180 degrees (or reflection through the origin). This transformation results in a congruent figure since the size and shape are preserved.

4. **Option #4: \((x,y)→(y,x)\)** - This is a reflection or flip over the line \(y = x\). It preserves shape and size, thus producing a congruent figure.

Based on the analysis, the option that yields a similar figure instead of a congruent figure is **Option #2**.

The correct response is Option **2**.