High School

Let \( L_1 \), \( L_2 \), and \( L_3 \) be three lines such that \( L_1 \) is perpendicular to \( L_2 \), and \( L_2 \) is perpendicular to both \( L_1 \) and \( L_3 \).

Then, the point which lies on \( L_1 \) is:

a) The point of intersection of \( L_2 \) and \( L_3 \)
b) The point of intersection of \( L_1 \) and \( L_3 \)
c) The point of intersection of \( L_1 \) and \( L_2 \)
d) The point of intersection of \( L_1 \), \( L_2 \), and \( L_3 \)

Answer :

c) The point of intersection of L₁ and L₂. The point on L₁ is the point of intersection of L₁ and L₂ due to their perpendicular relationship.

To solve this, note that since L₁ is perpendicular to L₂ and L₂ is perpendicular to both L₁ and L₃, these three lines intersect at a single point, making L₂ perpendicular to both L₁ and L₃ at a common intersection. Therefore, the point which lies on L₁ is:

This is due to the fact that if two lines are perpendicular, they intersect at a point. Here, L₁ and L₂ intersect at one point because they are perpendicular to each other.