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Since the dilatation is centred at the origin then multiply each of the coordinates of the vertices by the scale factor.

(- 4, 2 ) → (- 4, 2 ) → (- 2, 1 )

Similarly

(- 2, 8 ) → (- 1, 4 )

(2, 4 ) → (1, 2 )

(-2, 1), (-1, 4) and (1, 2)

Step-by-step explanation:

We are given a triangle with points (-4, 2), (-2, 8) and (2, 4) and we are to graph the image of the given triangle after a dilation with a scale factor of centered at the origin.

So, we will multiply the coordinates of each point by to get the points of the image after dilation.

(-4, 2) -->  

(-2, 8) -->  

(2, 4) -->  

Therefore, the coordinates of the image of the given figure after dilation will be (-2, 1), (-1, 4) and (1, 2).

12cm

the answer is d