Question

the larger triangle is the preimage and the smaller triangle is the image. which of the following represents the motion rule used to dilate the triangle? (x,y)→(1/2 x, 1/2 y) (x,y)→(x + 1/2,y + 1/2) (x,y)→(2x,2y) (x,y)→(x + 2,y + 2)

Explanation:

Step1: Recall dilation rule

Dilation about the origin has the form $(x,y)\to(kx,ky)$ where $k$ is the scale - factor. If $k> 1$, the figure is enlarged; if $0 < k<1$, the figure is reduced.

Step2: Analyze the given triangles

The larger triangle (pre - image) is reduced to the smaller triangle (image). So the scale - factor $k$ should be between $0$ and $1$.

Step3: Check each option

For option $(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$, the scale - factor $k = \frac{1}{2}$ which is between $0$ and $1$. For option $(x,y)\to(x+\frac{1}{2},y+\frac{1}{2})$, this is a translation. For option $(x,y)\to(2x,2y)$, the scale - factor $k = 2>1$ which represents an enlargement. For option $(x,y)\to(x + 2,y + 2)$, this is a translation.

Answer:

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