Select the correct name for the following line.
The Correct Answer and Explanation is:
The correct answer is: the first option — the one labeled with the line symbol over “EF” (↔).
Explanation:
In geometry, a line is defined as a straight one-dimensional figure that extends infinitely in both directions. It is typically named by two points that lie on the line and a symbol consisting of a line with two arrowheads over the two letters.
In the image:
- The figure shows two points, labeled E and F, with a straight line that extends infinitely in both directions — indicated by the arrows on both ends.
- The correct notation for a line that passes through two points and continues infinitely in both directions is EF↔\overleftrightarrow{EF}.
- This is the first answer choice in the list.
Let’s analyze the incorrect choices:
- The second choice uses the ray symbol (EF→\overrightarrow{EF}), which represents a ray — a figure that starts at point E and passes through F, continuing infinitely in one direction only. But the given figure shows arrows in both directions, not just one, so this cannot be correct.
- The third choice (EF←\overleftarrow{EF}) indicates a ray that starts at point F and goes through E, extending infinitely to the left — again, not matching the image.
Summary:
The given image represents a line, not a ray or a segment, as it extends infinitely in both directions. Hence, the correct name is line EF, notated as EF↔\overleftrightarrow{EF}, which is the first option.
