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

Question

1. (−1, 1) and (4, 4)
2. (−1, −1) and (−4, −4)
3. (1, −1) and (4, −4)
4. (−1, 1) and (−4, 4)

Answer 1

To find the reflected endpoints of the line segment with endpoints (1, 1) and (4, 4) across the y-axis, we need to negate the x-coordinates of each endpoint while keeping the y-coordinates unchanged.

Let's reflect each endpoint:

1. For the point (1, 1):

   • Reflecting across the y-axis: \((-1, 1)\)

2. For the point (4, 4):

   • Reflecting across the y-axis: \((-4, 4)\)

Therefore, the reflected endpoints are \((-1, 1)\) and \((-4, 4)\).

The correct answer is: 4. (−1, 1) and (−4, 4)