So when I create a triangle by using the star shape tool and only giving it three points. When I have my triangle, I duplicate it and make it smaller. I center them both up on the canvas, but they don't look centered. As you can see in the picture provided, the bottom has more of a width that the others. I've tried using the alignment tool and the smart guides. I do resize the triangle using shift so it doesn't mess up the shape too. What could be the cause of this?
The way you do it is based on the Bounding Box, and its centre is above the centre of the triangle.
If you know the distance between corresponding (outer) sides, you may Object>Path>Offset Path with a negative value equalling the distance.
If you know some other relation between the sizes, you may (Smart Guides are your friends):
1) Copy the original triangle,
2) Object>Path>Average (both), this will create a triangle with a side length of 0 at the centre, thus acting as a centre point,
3) Group both,
4) Copy the Group and set the size of the new triangle (set),
5) Drag the new set straight down by the centre until it coincides with the centre of the original triangle (Smart Guides say anchor),
6) Ungroup and delete the centre triangles.
It should if you have done all the above (and dragged sufficiently slowly along the vertical line shown by Smart Guides (you may hold Shift to keep vertical)), even if you have filled tringles (in which case Smart Guides seem to say intersect for some or no reason).
In any case, among the other more or less silly ways, if you know the reduction in radius or height, which is 1.5 times the radius, you may:
1) With the Transform Reference Point set to centre (default), copy the triangle and reduce the height, then move the copy down by 1/6 the change in height (or 1/4 the change in radius); the value may be subtracted from the Y value;
2) With the Transform Reference Point set to bottom, copy the triangle and reduce the height, then move the copy up by 1/3 the change in height (or 1/2 the change in radius); the value may be added to the Y value.
In which way do you reduce the size?
Unless you have CS6, you may also:
1) Select the triangle and apply the free Circumcircle script, se below,
2) Select both, copy, and reduce the size (the circumcircle is twice the radius or 4/3 the height),
3) Delete the circumcircles.
The free Circumcircle script, along with many other fine non CS6 scripts, is available here:
There are still other ways.
The whole point of everything that Jacob is trying to tell you is that the geometrical centre of any regular polygon that has an odd number of sides is not in the same place as the centre of its rectangular bounding box.
There are various ways of finding the geometrical centre (like this way using added anchors and guides):
but once you have found it you use it as the reference point for scaling with the Scale tool
I was looking forward to your median construction of the centroid, Steve.
It’s just a computerized version of what one was taught to do with a pair of compasses at primary school over fifty years ago. Still works :-)