Question

The line segment reflects across the y-axis. What are the new coordinates for the endpoints? How does the transformation affect the length of the line segment?

a) (-4, -8) and (4, 1); The transformation does not affect the length.
b) (-4, -8) and (-4, -1); The resulting segment is longer.
c) (4, 8) and (-4, -1); The transformation does not affect the length.
d) (4, 8) and (4, 1); The resulting segment is shorter.

Answer 1

When a line segment is reflected across the y-axis, only the sign of the x-coordinates changes, not the y-coordinates. The length of the line segment remains unchanged because reflections are isometries.

Step-by-step explanation:

Reflecting a line segment across the y-axis involves changing the sign of the x-coordinates of the endpoints, while the y-coordinates remain the same. For example, reflecting the point (-4, -8) across the y-axis would result in the point (4, -8), and reflecting the point (4, 1) would give (-4, 1).

Regarding the length of the line segment, reflections are a type of isometry, which means that they preserve distances. Thus, when a line segment reflects across the y-axis, the length of the line segment does not change.

The correct answer is:

• a) (-4, -8) and (4, 1); The transformation does not affect the length.