Question

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

(−1, 1)
and (−4, 4)
left parenthesis negative 1 comma 1 right parenthesis and left parenthesis negative 4 comma 4 right parenthesis

(−1, 1)
and (4, 4)
left parenthesis negative 1 comma 1 right parenthesis and left parenthesis 4 comma 4 right parenthesis

(1, −1)
and (4, −4)
left parenthesis 1 comma negative 1 right parenthesis and left parenthesis 4 comma negative 4 right parenthesis

(−1, −1)
and (−4, −4)

Answer 1

To find the reflections of the endpoints of a line segment across the y-axis, we need to change the sign of the x-coordinates while keeping the y-coordinates the same.

The endpoints of the line segment are (1, 1) and (4, 4).

1. For the point (1, 1), the reflection across the y-axis is:
- x-coordinate: 1 becomes -1
- y-coordinate: stays the same, so it remains 1
- Reflected point: (-1, 1)

2. For the point (4, 4), the reflection across the y-axis is:
- x-coordinate: 4 becomes -4
- y-coordinate: stays the same, so it remains 4
- Reflected point: (-4, 4)

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

The correct response is:
(−1, 1) and (−4, 4) left parenthesis negative 1 comma 1 right parenthesis and left parenthesis negative 4 comma 4 right parenthesis.