A dilation has center (0, 0). Find the image of the point B (3, -5) for the scale factor of 2.

Question

anonymous · Answer

The image will have coordinates that are twice as far from the centre as B is, as the factor is 2.  

That is, you take the coordinates of point B, subtract those of the centre to find out the distance between them  and then multiply this distance by 2, as that is the factor.  But you want doubled the distance from the centre and so you add it back to the centre coordinates to get the image.  

In other words for the $x$ coordinate, the distance between the centre and B is  $(3-0)=3$  so the image will have to be a distance of 2*3 = 6 from the centre.  As the centre has an x coordinate of 0, the image will have an x coordinate of 0+6=6.  

Similarly for the $y$ coordinate.