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)→(2 1/2 x, 2 1/2 y) (x, y)→(2/5 x, 2/5 y) (x, y)→(x - 3, y - 3)

Explanation:

Step1: Find the radius of each circle

Count the grid - units from the center (origin) to the circle. For Circle 1, the radius $r_1 = 2$. For Circle 2, the radius $r_2=5$.

Step2: Determine the scale factor of dilation

The scale factor $k$ of a dilation is given by the ratio of the radii of the dilated figure to the original figure. So $k=\frac{r_2}{r_1}=\frac{5}{2}=2\frac{1}{2}$.

Step3: Identify the dilation rule

In a dilation centered at the origin, the rule is $(x,y)\to(kx,ky)$. Since $k = 2\frac{1}{2}$, the rule is $(x,y)\to(2\frac{1}{2}x,2\frac{1}{2}y)$.

Answer:

$(x,y)\to(2\frac{1}{2}x,2\frac{1}{2}y)$