Question 1202939: Determine if the two figures are congruent and explain your answer using transformations. (10 points)
Figure ABCD is shown. A is at negative 1, 1. B is at negative 3, 2. C is at negative 4, 4. D is at negative 2, 6. Figure EFGH is shown. E is at 2, 0. F is at 4, 1. G is at 5, 3. H is at 3, 5.
Found 2 solutions by Seutip, greenestamps:
Answer by Seutip(231)   (Show Source):
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
The other tutor didn't draw either figure correctly....
The two figures appear to be congruent. Showing that in fact they are algebraically can be done by seeing how the change from A to B compares to the change from E to F,and so on. That is an easy task; I won't take the time to do that in my response.
The transformations to get EFGH from ABCD are, in either order, a translation and a horizontal flip. (Or we could do a different more complicated sequence of transformations....)
I will do a horizontal flip (about the y axis) and then a translation.
(1) Reflect about the y axis:
From the diagram we can see that the two figures are congruent, and that the second transformation is a translation 1 unit right and 1 unit down.
ANSWERS:
The two figures are congruent.
One sequence of transformation that gets from ABCD to EFGH is (1) reflect about the y axis and (2) translate right 1, down 1
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