To determine if figure T is a reflection of figure S across the x-axis, we need to check if the coordinates of points in figure T are the negatives of the corresponding points in figure S when reflected across the x-axis.
For figure S, the coordinates of points are:
- A(1, 1)
- B(6, 1)
- C(4, 5)
- D(5, 6)
- E(2, 6)
- F(3, 5)
When we reflect these points across the x-axis, the new coordinates will be:
- A'(1, -1)
- B'(6, -1)
- C'(4, -5)
- D'(5, -6)
- E'(2, -6)
- F'(3, -5)
For figure T, the coordinates of points are:
- A(2, -1)
- B(5, -1)
- C(4, -2)
- D(6, -5)
- E(1, -5)
- F(3, -2)
Now we compare the corresponding points:
- A: S A'(1, -1) and T A(2, -1) - not a match.
- B: S B'(6, -1) and T B(5, -1) - not a match.
- C: S C'(4, -5) and T C(4, -2) - not a match.
- D: S D'(5, -6) and T D(6, -5) - not a match.
- E: S E'(2, -6) and T E(1, -5) - not a match.
- F: S F'(3, -5) and T F(3, -2) - not a match.
Since none of the points in figure T correspond to the reflected coordinates of points in figure S, figure T is not a reflection of figure S across the x-axis.
Therefore, the answer is 2 for no.