To determine whether figure T is a reflection of figure S across the x-axis, we can analyze the coordinates of the points in both hexagons.
Figure S (First Quadrant):
- A(1, 1)
- B(6, 1)
- C(4, 5)
- D(5, 6)
- E(2, 6)
- F(3, 5)
Figure T (Fourth Quadrant):
- A(2, -1)
- B(5, -1)
- C(4, -2)
- D(6, -5)
- E(1, -5)
- F(3, -2)
To reflect figure S across the x-axis, the y-coordinates of the points should change signs while the x-coordinates remain the same. So, let's find the reflection of each point in figure S:
- A(1, 1) → A'(1, -1)
- B(6, 1) → B'(6, -1)
- C(4, 5) → C'(4, -5)
- D(5, 6) → D'(5, -6)
- E(2, 6) → E'(2, -6)
- F(3, 5) → F'(3, -5)
Now, let’s compare the reflected points to the points in figure T:
- A'(1, -1) does not match A(2, -1)
- B'(6, -1) does not match B(5, -1)
- C'(4, -5) does not match C(4, -2)
- D'(5, -6) does not match D(6, -5)
- E'(2, -6) does not match E(1, -5)
- F'(3, -5) does not match F(3, -2)
Since none of the points in figure T match the reflection points from figure S, figure T is not a reflection of figure S across the x-axis.
Therefore, the answer is 2 (no).