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 whether figure T is a reflection of figure S across the x-axis, we can compare the coordinates of the points of both hexagons.

The coordinates of the points in figure S (upper S) are:
- A: (1, 1)
- B: (6, 1)
- C: (4, 5)
- D: (5, 6)
- E: (2, 6)
- F: (3, 5)

When reflecting across the x-axis, the y-coordinates of each point will have the opposite sign. Therefore, the reflected points would be:
- A': (1, -1)
- B': (6, -1)
- C': (4, -5)
- D': (5, -6)
- E': (2, -6)
- F': (3, -5)

The coordinates of the points in figure T (upper T) are:
- A: (2, -1)
- B: (5, -1)
- C: (4, -2)
- D: (6, -5)
- E: (1, -5)
- F: (3, -2)

Now, we can see if the coordinates for T match the reflected coordinates of S:
- 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 the points do not match, figure T is not a reflection of figure S across the x-axis.

Therefore, the answer is **2** (no).