Answer: No, Titus is incorrect.
Step-by-step explanation: Two shapes are <u>congruent</u> when they have the same size and shape, but one is created of rotation, reversion or translation of the other.
So, hexagons FEDCBA and F'E'D'C'B'A' are congruent because they have the same size and shape, however they are reversed and translated from each other, i.e.:
Comparing the coordinates of both hexagons:
F (-6,6) → F' (6, -4)
A (-10,6) → A' (10,-4)
E (-4,4) → E' (4, -6)
B (-12,4) → B' (12, -6)
D (-6,2) → D' (6, -8)
C (-10,2) → C' (10, -8)
We notice that the transformation necessary to transform FEDCBA into F'E'D'C'B'A' is
- multiply x-coordinate by (-1);
- subtract y-coordinate by 10;
Therefore, it is (x,y) → ( -x, y-10).
So, Titus is incorrect about the transformations that prove the hexagons are congruent.
