Question

circle 1 was dilated with the origin as the center of dilation to create circle 2. which rule best represents the dilation applied to circle 1 to create circle 2? (x,y)→(1/5 x,1/5 y) (x,y)→(x - 4,y - 4) (x,y)→(x + 4,y + 4) (x,y)→(5x,5y)

Explanation:

Step1: Observe circle size change

Dilation is a transformation that changes the size of a figure. If a figure is enlarged, the scale factor is greater than 1. If it is reduced, the scale factor is between 0 and 1. Here, Circle 2 is larger than Circle 1, so the scale - factor of dilation is greater than 1.

Step2: Analyze coordinate transformation rules

The rule \((x,y)\to(kx,ky)\) represents a dilation centered at the origin with a scale factor \(k\). Rules \((x,y)\to(x - 4,y - 4)\) and \((x,y)\to(x + 4,y + 4)\) are translations, not dilations. The rule \((x,y)\to(\frac{1}{5}x,\frac{1}{5}y)\) is a reduction (scale factor \(k=\frac{1}{5}<1\)). The rule \((x,y)\to(5x,5y)\) is an enlargement (scale factor \(k = 5>1\)).

Answer:

\((x,y)\to(5x,5y)\)