A line segment has endpoints (1, 1)

Question

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 negative 1 right parenthesis and left parenthesis negative 4 comma negative 4 right parenthesis

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

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

Answer 1

When reflecting a point across the y-axis, the x-coordinate of the point changes sign while the y-coordinate remains the same.

Given the endpoints of the line segment:

• Point A: \( (1, 1) \)
• Point B: \( (4, 4) \)

Let's find the reflected endpoints:

1. Reflection of point A \( (1, 1) \):

   • New x-coordinate: \( -1 \)
   • New y-coordinate: \( 1 \)
   • Reflected point A: \( (-1, 1) \)

2. Reflection of point B \( (4, 4) \):

   • New x-coordinate: \( -4 \)
   • New y-coordinate: \( 4 \)
   • Reflected point B: \( (-4, 4) \)

Thus, the reflected endpoints are: \[ (-1, 1) \quad \text{and} \quad (-4, 4) \]

So, the correct response is: (−1, 1) and (−4, 4).