Question

rayhan thinks that a dilation with a scale factor of 1 would always leave a figure such as the triangle below unchanged. select all of the centers of dilation that support rayhans claim. a (-4,4) b (-2,0) c (2,0)

Explanation:

Step1: Recall dilation property

A dilation with a scale - factor of 1 will leave a figure unchanged regardless of the center of dilation. This is because when we use the dilation formula $(x,y)\to k(x - a)+a,k(y - b)+b$ (where $(a,b)$ is the center of dilation and $k$ is the scale - factor), when $k = 1$, we have $(x,y)\to1\times(x - a)+a,1\times(y - b)+b=(x,y)$.

Step2: Analyze each option

For any point $(a,b)$ chosen as the center of dilation, when the scale - factor $k = 1$, the figure will remain the same. So all of the given points A$(-4,4)$, B$(-2,0)$ and C$(2,0)$ will support Rayhan's claim.

Answer:

A. $(-4,4)$, B. $(-2,0)$, C. $(2,0)$