Please help! (I don't know if this comes under Geometry but whatever)

[Devin Shen]

Thank you very much!!

 

[Devin Shen]

I have no idea how to do this question at all, and can only find a few values for certain lines, as shown in the image.

 

[Dr.Peterson]

View attachment 24202

Thank you very much!!

Since the problem is about vectors (which could go under either geometry or algebra, by the way), I would label vectors on the diagram, using arrows and names, like this:


Now the key idea is that P is the intersection of AB and NM. There are many ways to use this, but what I did is to state that AP = xAB and NP = yNM, and use each fact to express OP in terms of x and y. Setting these two expressions equal, I solved for x and y; x will give you what you are asked for.

Again, others may have very different ways to carry out the details.

 

[Devin Shen]

Thank you so so much!! I understand now, and I have worked out the answer.