Answer
To graph the image of the triangle after a dilation with a scale factor of 2 centered at the origin, we start with the coordinates of the triangle, which are (0, 0), (4, -4), and (-4, -2). The dilation transformation is given by the formula ((x,y) rightarrow (kx, ky)). In this case, with a scale factor of 2, we calculate the new coordinates as follows: ((0,0) rightarrow (2 times 0, 2 times 0)), ((4,-4) rightarrow (2 times 4, 2 times -4)), and ((-4,-2) rightarrow (2 times -4, 2 times -2)). Thus, the new coordinates of the dilated triangle are (0,0), (8,-8), and (-8,-4).
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