Dilation by a factor of 3 about point P moves A to a position that is 3 times as far from P. This is shown in the attachment.
Dilation is always along a line through the original point and the center of dilation.
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(The lines are there in the attachment simply to show you that the image position is 3 times the distance from P that the original position is. They are not part of the dilation or the image.)