Geometry help please with sets?

Question

I asked this before, but it got buried. I have a line l that intersects line m at point A. Line l contains the points A and B. Line m contains the points A and C.

1. Line AB ∩ Line AC = ?

I wrote {A}

2. Line AC ∩ Line BC = ?

I wrote null-set, because there is no line BC! But I am not sure about this one. What if they wanted me to imagine a line BC? Should I say {B} or {}?

Thank you

Sue

Answer 1

Part 1: correct.

two lines have at most 1 point in common.

The two meanings of the word intersection

come together in this problem.

Part 2:

It seems the statement of the question has

just created line BC.  You might answer:

. . . The points B and C implicitly define a third line,

. . . the intersection of which with line AC = {C}.

That covers all bases.

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