Question

In geometry, if a line is passing through a point not on line l, how many lines can be drawn that are perpendicular to line l?

A) Exactly one
B) Two or more
C) None
D) It depends on the location of the point

Answer 1

Option A is the correct option. In geometry, exactly one line can be drawn perpendicular to a given line l from a point not on line l, based on Euclidean postulates.

Step-by-step explanation:

In geometry, when considering a line passing through a point that is not on line l, the principle to determine how many perpendicular lines can be drawn to line l from that point comes from the fact that in Euclidean space, through a given point not on a given line, there is exactly one line that can be drawn perpendicular to the given line. This stems from the unique properties of perpendicular lines in a plane. Therefore, the answer to the question is A) Exactly one.

Here is a step-by-step explanation to support this concept:

1. Consider line l and a point P that is not on line l.
2. To draw a perpendicular line from point P to line l, you need to take into account the definition of perpendicular lines, which are lines that intersect to form right angles (90 degrees).
3. According to the postulates of Euclidean geometry, given a line and a point not on that line, there exists a unique line through the point that is perpendicular to the original line. This new line will intersect the original line at one point, creating a right angle between the two.
4. Thus, it is not possible to draw more than one line from point P to line l that would make a right angle with line l, as that would contradict the unique perpendicular postulate.