If triangle ABC is defined by the coordinates A(-4,-4), B(2,-2), C(0,4) is dilated by a scale factor of 1/2, with resulting vertex A’ at (-2,-2). What is the center of the dilation?
A. (0,0)
B. (0,2)
C. (0,4)
D. (-4,-4)

For center of dilation Q, the image of a point A after dilation by a factor of k is ... A' = kA + (k-1)Q Then for points A, A', and dilation factor k, the center of dilation can be found to be ... (A' -kA)/(k-1) = Q

Here, that is ... Q = ((-2, -2) -(1/2)(-4, -4))/(1/2 -1) = (0, 0)/(-1/2)

Q = (0, 0)

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If triangle ABC is defined by the coordinates A(-4,-4), B(2,-2), C(0,4) is dilated by a scale factor of 1/2, with resulting vertex A’ at (-2,-2). What is the center of the dilation? A. (0,0) B. (0,2) C. (0,4) D. (-4,-4)

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If triangle ABC is defined by the coordinates A(-4,-4), B(2,-2), C(0,4) is dilated by a scale factor of 1/2, with resulting vertex A’ at (-2,-2). What is the center of the dilation?
A. (0,0)
B. (0,2)
C. (0,4)
D. (-4,-4)