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In mathematics, a dilation is a transformation that changes the size of an object without changing its shape. To find the coordinates for the dilation of a triangle, we first determine the scale factor. In this case, the scale factor is 1/2, which means the triangle will be reduced to half its original size. The center of dilation is the origin, which is the point (0,0). Using the scale factor and the coordinates of the original triangle's vertices, we can find the new coordinates by multiplying each original coordinate by the scale factor. The new vertices for the dilated triangle with the given scale factor and center of dilation are (0,0), (0,1), and (2,0).