If the vertices of quadrilateral ABCD are A(1,1), B(-2,3), C(-4,-1), and D(2,-3), and the quadrilateral is dilated so that it's perimeter is 2 times the original perimeter, what would the vertex matrix look like?
math - Reiny, Thursday, January 1, 2009 at 11:44pm
Several questions are gnawing at me as I read your question.
1. What form does your dilation take?
you could keep one point in its present position and simply double the length of each side.
e.g. keep B(-2,3) but move A to A1(4,-1) so that A becomes the midpoint of BA1.
I would be relatively easy to work your way around in the same way for the other sides.
Of course you could do this again by keeping point A constant, etc.
Another way would be to find the intersection of the two diagonals, call it F, and then joining F to the original vertices and extending FA,FB,FC,and FD its own length.
2. Some of this can be done with vector geometry, but do you know how to work with vectors?
3. I am not sure what you mean by a "vertex matrix".
4. What course level is this? Is it simply analytical geometry?
math - Anonymous, Friday, January 2, 2009 at 12:02am
1. not sure
2. Don't remember but the book says to do it with matrices.
3. My book says a vertex matrix is a matrix into which the coordinates of a polygon's matrices are placed.
4. Algebra 2 - Transformations with matrices
math - Reiny, Friday, January 2, 2009 at 12:15am
ok, then keeping B as it is, I found
each of my new sides are twice as long as the old ones, but the new lines are parallel to the original
e.g. AD is parallel to A1D1
math - Anonymous, Friday, January 2, 2009 at 12:21am
Yes, but how would I represent this in a matrix?