Geometry question. How to calculate the minimum value of line segment BM.

[Arismaotle]

The question is in the attachment.
Quick translation(please forgive my poor English):

Point A(-2,2√3)，Point B(1,0). P is a moving point along x-axis. Line QP is perpendicular to the line AP. M is the middle point of the line PQ. Please calculate the minimum value of line segment BM.

 

[Deleted member 4993]

The question is in the attachment.
Quick translation(please forgive my poor English):

Point A(-2,2√3)，Point B(1,0). P is a moving point along x-axis. Line QP is perpendicular to the line AP. M is the middle point of the line PQ. Please calculate the minimum value of line segment BM.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

Point A(-2,2√3)，Point B(1,0). P is a moving point along x-axis. Line QP is perpendicular to the line AP. M is the middle point of the line PQ. Please calculate the minimum value of line segment BM.

 

[Dr.Peterson]

The question is in the attachment.
Quick translation(please forgive my poor English):

Point A(-2,2√3)，Point B(1,0). P is a moving point along x-axis. Line QP is perpendicular to the line AP. M is the middle point of the line PQ. Please calculate the minimum value of line segment BM.

I don't think you mean that QP is perpendicular to AP; the picture says that QA is perpendicular to AP.

Here is the (rather poor) translation I get from one site:

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I suspect that what this really means is "the perpendicular line to AP at A intersects the y-axis at point Q".

You put this under geometry, but it sounds like a place to use calculus. Is that available to you? I haven't tried solving this yet, before knowing what you can do or what you have done.

 

[Otis]

Line QP is perpendicular to the line AP

Hi. Line AQ is perpendicular to line AP.

Is point P allowed to be on the negative x-axis?



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