Create your own quadrilateral on a coordinate plane. This figure may be a parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid, or kite. Provide the coordinates of the vertices for the quadrilateral you designed.

Question

anonymous · Answer

Provide the coordinates of a quadrilateral congruent to the quadrilateral you created. Explain why these figures are congruent.
 
Provide the coordinates of a quadrilateral similar to the quadrilateral you created. Explain why these figures are similar.

anonymous · Answer

Well, if you're not interested in bragging rights, go for the simple case:  square determined by (0,0), (1,0), (1,1), and (0,1).  A similar figure is determined by (0,0), (2,0), (2,2), and (0,2).  Both are squares with sides on the x and y axes, vertex at the origin.  The first has sides of length one, the second has sides length two.

anonymous · Answer

i don't mean to be pushy but can you give me different coordinates, or will this work (2,2), (2,4), (4,4), and (4,2) and then the same coordinates on the negative side?

istim · Answer

Really, I'm thinking: Make a square, note the points, translate square (and points) around, note new location of points. Ta-da!

anonymous · Answer

Yeah, yours will work.  I just re-read the question, and it seems I answered the last part of it, while skipping the middle part.  Your plan to take the negatives of all the coordinates is a good one to get a second congruent figure.  The one I gave you is really the answer for the last part of the problem, giving a second figure that is similar to the first.

anonymous · Answer

i put this as my final answer:

coordinates for congruent squares:  
(2,2), (2,4), (4,4), (4,2) AND (-2,2), (-2,4), (-4,4), (-4,2) Side lengths are the same; angles are the same.
coordinates for similar squares:
(0,0), (1,0), (1,1), (0,1). and (0,0), (2,0), (2,2), (0,2) Both are squares with sides on the x and y axes, vertex at the origin. The first has sides of length one, the second has sides length two.