# changing coordinate system

I'm currently trying to transform a system by scaling it on x and y axis and have some uncertainty. I have the general concept that scaling works as such:

My original box has corners at (0, 0) and (3, 2) and I'm asked to scale the x axis by 3 and the y axis by -2.

Is this what the correct solution would look like (with corners at (0,2) and (6,-2))?

Given the points you have, no. The new rectangle will be defined by the points (0, 0) and (6, -4). The point on the origin will not scale to a new position where are the other point you have will. Scaling by -2 in the y will flip the rectangle so instead of having a point in the bottom left and top right it will now be in the top left and bottom right.

• Got it. Is this what it would look like? – Kermit Mar 30 '13 at 18:06
• Yes it is. Best is to remember that scaling will move things away (or if less than 0 then towards) the origin. Since a point is already at the origin it will stay there. – CodeNeko Mar 30 '13 at 18:11