Question

se 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
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 every point of figure T is the reflection of the corresponding point from figure S.

For figure S, the points are:
- A(1, 1) → reflected to A'(1, -1)
- B(6, 1) → reflected to B'(6, -1)
- C(4, 5) → reflected to C'(4, -5)
- D(5, 6) → reflected to D'(5, -6)
- E(2, 6) → reflected to E'(2, -6)
- F(3, 5) → reflected to F'(3, -5)

For figure T, the points are:
- A(2, -1)
- B(5, -1)
- C(4, -2)
- D(6, -5)
- E(1, -5)
- F(3, -2)

Now, let's compare the coordinates of figure T with the reflected coordinates of figure S:
- A'(1, -1) and A(2, -1) → Not the same
- B'(6, -1) and B(5, -1) → Not the same
- C'(4, -5) and C(4, -2) → Not the same
- D'(5, -6) and D(6, -5) → Not the same
- E'(2, -6) and E(1, -5) → Not the same
- F'(3, -5) and F(3, -2) → Not the same

Since none of the points from figure T match the reflected points from figure S, we conclude that figure T is not a reflection of figure S across the x-axis.

The answer is **2** for no.