Question

Question 4

Titus is asked to prove hexagon FEDCBA is congruent to hexagon
F'E'D'C'B'A' in the graph below. Titus thinks that if he transforms hexagon
FEDCBA by (x, y) - (x + 16, y - 10) he can show the two figures are
congruent. Is he correct? Explain why or why not. If Titus is incorrect, what
series of transformations will correctly prove FEDCBA F'E'D'C' B'A'!
I need ASAPPPP

Answer 1

Answer: No, Titus is incorrect.

Explanation: Two shapes are congruent 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.