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: Identify dilation rule concept

Dilation with center at origin has rule $(x,y)\to(kx,ky)$ where $k$ is scale - factor.

Step2: Observe circle sizes

Circle 2 is larger than Circle 1, so scale - factor $k> 1$.

Step3: Analyze options

Options $(x,y)\to(\frac{1}{5}x,\frac{1}{5}y)$ has $k = \frac{1}{5}<1$ (shrinking), $(x,y)\to(x - 4,y - 4)$ and $(x,y)\to(x + 4,y + 4)$ are translations. Option $(x,y)\to(5x,5y)$ has $k = 5>1$ (enlarging).

Answer:

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