A line segment with a length of 16 units is reflected across the y-axis, then translated 5 units down on a coordinate plane, resulting in a new segment.

Question

What is the length of this new line segment?
Answer

units

Answer 1

The length of a line segment is a measure of distance between its two endpoints. When a line segment is reflected across the y-axis and then translated, the length of the segment remains unchanged.

1. Reflection across the y-axis: This transformation only changes the x-coordinates of the points on the segment to their negatives, leaving the distance between the two points unchanged.

2. Translation (5 units down): This transformation shifts the y-coordinates of the points on the segment lower by 5 units, but again does not affect the distance between the endpoints.

Since neither of these transformations changes the length of the segment, the length of the new line segment after reflection and translation remains the same as the original segment.

Therefore, the length of the new line segment is:

16 units.