Use the image to answer the question.

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.(1 point)

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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 the points in figure T correspond to the reflection of the points in figure S.

The coordinates of figure S (hexagon S) are:

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

The reflection of a point (x, y) across the x-axis is given by (x, -y). Therefore, we can calculate the reflected points for figure S:

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

Now, let's compare the coordinates of figure T (hexagon T) with the reflected points:

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

As we can see, the coordinates of figure T do not match the reflected points of figure S. Therefore, figure T is not a reflection of figure S across the x-axis.

The answer is 2 (no).