Answer :
The point that lies on line L1 is the point of intersection of L1 and L2 since L1 is perpendicular to L2, and the intersection of two perpendicular lines lies on both lines. Therefore, the correct answer is option c) The point of intersection of L1 and L2.
Considering three lines: L1, L2, and L3, with L1 perpendicular to L2, and L2 perpendicular to both L1 and L3, the question concerns which point lies on L1.
It's given that two lines perpendicular to a third line have points equidistant from each other if the points are equidistant from the third line. In this scenario, the point of intersection of L1 and L2 is the point that lies on L1.
Being perpendicular to L2, L1 would intersect it at some point, which is by definition a point on L1.
Moreover, since L3 is also perpendicular to L2, it would intersect L2 at a point, but this does not determine its intersection with L1.
The third theorem suggests that a perpendicular at the intersection point of two lines would be perpendicular to every line in the plane passing through that point, which applies here and confirms that the intersection of L1 and L2 is the pertinent point on L1.
Therefore, the correct answer is option c) The point of intersection of L1 and L2.
Final answer:
The point lies on line L1 where it intersects with line L2, since both L1 and L3 are perpendicular to L2, indicating point c) The point of intersection of L1 and L2 as the answer.
Explanation:
Given that line L1 is perpendicular to line L2, and line L2 is also perpendicular to line L3, we can use geometric theorems to determine the relationships between these lines. According to the theorems, if two lines (L1 and L3) are perpendicular to a third line (L2), then they must lie in the same plane and intersect at a point on that third line, which is named the pole of those lines. Therefore, the point which lies on L1 would be the point of intersection between L1 and L2, which is also the pole of those lines. Consequently, the correct answer is c) The point of intersection of L1 and L2.
