Question

21 trapezoid mnop is dilated using the origin as the center of dilation to create trapezoid mnop. what rule best represents the dilation applied to trapezoid mnop to create trapezoid mnop? a (x, y)→(5x, 6y) b (x, y)→(5x, 3y) c (x, y)→(3x, 3y) d (x, y)→(3x, 6y)

Explanation:

Step1: Recall dilation rule

A dilation centered at the origin has the rule $(x,y)\to(kx,ky)$ where $k$ is the scale - factor. In a dilation, all coordinates of the original figure are multiplied by the same non - zero scale factor $k$ to get the coordinates of the dilated figure.

Step2: Check the options

We need to find a single scale factor that multiplies both $x$ and $y$ coordinates. Options A, B, and D have different scale factors for $x$ and $y$ which is not correct for a dilation centered at the origin. Option C: $(x,y)\to(3x,3y)$ has the same scale factor $k = 3$ for both $x$ and $y$ coordinates.

Answer:

C. $(x,y)\to(3x,3y)$