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.

Question

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 analyze the coordinates of the points in both hexagons.

Figure S (First Quadrant):

1. A(1, 1)
2. B(6, 1)
3. C(4, 5)
4. D(5, 6)
5. E(2, 6)
6. F(3, 5)

Figure T (Fourth Quadrant):

1. A(2, -1)
2. B(5, -1)
3. C(4, -2)
4. D(6, -5)
5. E(1, -5)
6. 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:

1. A(1, 1) → A'(1, -1)
2. B(6, 1) → B'(6, -1)
3. C(4, 5) → C'(4, -5)
4. D(5, 6) → D'(5, -6)
5. E(2, 6) → E'(2, -6)
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).