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 does not change the size or shape of a figure regardless of the center of dilation. The distance from each point in the original figure to the center of dilation is multiplied by the scale - factor. When the scale - factor \(k = 1\), the image of each point \(P(x,y)\) with respect to a center of dilation \(C(h,k)\) is given by the formula \(P'(x',y')=(h + k(x - h),k + k(y - k))\). Substituting \(k = 1\) into the formula, we get \(P'(x',y')=(h+(x - h),k+(y - k))=(x,y)\). So, for any center of dilation, a dilation with a scale - factor of 1 leaves the figure unchanged.

Answer:

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