Question

A line segment has endpoints (1, 1) ( 1, 1 ) and (4, 4) ( 4, 4 ) . Demonstrating the properties of
reflections across the -axis, what are the reflected endpoints?(1 point)

(1, − 1) ( 1, − 1 ) and (4, − 4) ( 4, − 4 )
(−1, 1) ( −1, 1 ) and (4, 4) ( 4, 4 )
(−1, − 1) ( −1, − 1 ) and (−4, − 4) ( −4, − 4 )
(−1, 1) ( −1, 1 ) and (−4, 4) ( −4, 4 )

Answer 1

To find the reflected endpoints of the line segment across the x-axis, we need to apply the reflection transformation. When a point \((x, y)\) is reflected across the x-axis, its y-coordinate changes sign, while its x-coordinate remains the same. Thus, the reflection of the point is given by \((x, -y)\).

The original endpoints of the line segment are:
1. \( (1, 1) \)
2. \( (4, 4) \)

Now, we reflect each endpoint:

1. For the point \( (1, 1) \):
- The reflection is \( (1, -1) \).

2. For the point \( (4, 4) \):
- The reflection is \( (4, -4) \).

Thus, the reflected endpoints of the line segment are \( (1, -1) \) and \( (4, -4) \).

Therefore, the correct answer is:
**(1, −1) and (4, −4)**.