A dilation is specified by 4 different collinear points A1,B1,A2,B2, where A1 maps to A2, B1 to B2: Choose a point H1 not on the line A1B1 and draw the triangle A1H1B1. Then the parallel to A1H1 through A2 and the parallel to B1H1 through B2 intersect in a point H2. If A1A2 and H1H2 are parallel, the dilation is a translation, otherwise (as is the case in the picture) it is a central dilation.
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KlioKlein