Question

Use the image to answer the question.
A coordinate plane shows two plotted irregular hexagons in the first and fourth quadrants. The coordinate plane shows both the x-axis and y-axis ranging from negative 7 to 7 in unit increments. The first quadrant shows a solid line irregular hexagon labeled upper S, formed by connecting the following points in the given order: point upper A is left parenthesis 1 comma 1 right parenthesis; point upper B left is parenthesis 6 comma 1 right parenthesis; point upper C is left parenthesis 4 comma 5 right parenthesis; point upper D is left parenthesis 5 comma 6 right parenthesis; point upper E is left parenthesis 2 comma 6 right parenthesis; and point upper F is left parenthesis 3 comma 5 right parenthesis. The hexagon is complete with point upper F connecting with point upper A. The fourth quadrant shows a dotted line irregular hexagon labeled upper T formed by connecting the following points in the given order: point upper A is left parenthesis 2 comma negative 1 right parenthesis; point upper B is left parenthesis 5 comma negative 1 right parenthesis; point upper C is left parenthesis 4 comma negative 2 right parenthesis; point upper D is left parenthesis 6 comma negative 5 right parenthesis; point upper E is left parenthesis 1 comma negative 5 right parenthesis; and point upper F is left parenthesis 3 comma negative 2 right parenthesis. The hexagon is complete with point upper F connecting with point upper A.
Is figure T a reflection of figure S across the x
-axis? Choose 1 for yes and 2 for no.

Answer 1

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:

1. **A**: S A'(1, -1) and T A(2, -1) - not a match.
2. **B**: S B'(6, -1) and T B(5, -1) - not a match.
3. **C**: S C'(4, -5) and T C(4, -2) - not a match.
4. **D**: S D'(5, -6) and T D(6, -5) - not a match.
5. **E**: S E'(2, -6) and T E(1, -5) - not a match.
6. **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**.