Question

Observe parallelogram ABCD plotted on the coordinate plane below.



Part I: Provide the coordinates of a parallelogram A’B’C’D’ that is congruent to parallelogram ABCD. Explain why these figures are congruent.

Part II: Provide the coordinates of a parallelogram A’’B’’C’’D’’ that is similar to parallelogram ABCD. Explain why these figures are similar.

Answer 1

i have no idea how to even do this...

Answer 2

For a congruent parallelogram (A'B'C'D'), shift the entire figure in any direction. Ex: the current location is:
A (-7,3)
B (-5,7)
C (1,7)
D (-1,3)
now, if we shift all these points 1 unit in the x direction, we get
A' (-6,3)
B' (-4,7)
C' (2,7)
D' (0,3)

for a similar parallelogram, divide the distance between a point (let's say point D) and the other points by a factor (let's say 2)
This gives:
A'' (-4,3)
B'' (-3,5)
C'' (0,5)
D'' (-1,3)

hope it makes sense! :-)

Answer 3

okay so i get the congruent part but not the similar part

Answer 4

I can't think of a better way to explain. Sorry!

Answer 5

Its okayy @BTaylor

Answer 6

@SmoothMath could yo explain to me how to get the similar coordinates?

Answer 7

Sure =) So, look at your original parallelogram and think of making it this way.
You pick a corner, let's do A. From A, you draw a line to B.
Here's where you ask yourself a question, "How do I draw that line?"
Answer: From A, go 2 right, 4 up
Now you draw a line from B to C. Ask yourself the question again.
Answer: From B, go 6 right
Draw a line from C to D. Ask yourself the question one last time:
Answer: From C, go 2 left, 4 down.

So what this gives you is instructions for creating a CONGRUENT parallelogram.
Pick a new point A'
From A', go 2 right, 4 up
From B', go 6 right
From C', go 2 left, 4 down
Connect D' to A'

Answer 8

So that's one way that you can create a congruent parallelogram, which isn't the question you asked me, but if you can do that, it makes creating a similar parallelogram pretty simple.

Answer 9

So does that process make sense to you?

Answer 10

yea, so instead of going 2 right 4 up, we could multiply that by 2 and go 4 right and 8 up, and by doing this to all of them it creats a similar tfigure?
@SmoothMath

Answer 11

Haha you got ahead of me, but yes. And you can actually choose any number you want and multiply the whole thing. So, for example, I could choose 3 and multiply the whole instructions by 3 to get

Pick a new point A'
From A', go 6 right, 12 up
From B', go 18 right
From C', go 6 left, 12 down
Connect D' to A'

Answer 12

Or I could multiply the whole instructions by (1/2) to get
Pick a new point A'
From A', go 1 right, 2 up
From B', go 3 right
From C', go 1 left, 2 down
Connect D' to A'

Answer 13

okay! i get it! thanks so much(:

Answer 14

My pleasure =)