Shortest distance from one point to a line segment

S_100

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Sep 27, 2019
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Question is as inserted in image.
It asks to find shortest distance from A to line segment PC.

I know that this line must be perpedicular to PC, however, how can I deduce, by looking at the question intially, that the perpedicular line from A to PC will be on a point halfway of PC, (bisects PC)?
 

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Jomo

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Dec 30, 2014
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How do you know it will be halfway? If it is, then you need to prove it and then find that point.
Do you know the equation of line PC (first you will need to state where the origin is or some other point). Do you know where point A is?
You have 15 posts so you know that you have to show us your work. Just making some conjecture is not enough. Come on, give it a try. At least anwser the questions I posed.
 

Subhotosh Khan

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2019-11-05.png
Question is as inserted in image.
It asks to find shortest distance from A to line segment PC.

I know that this line must be perpendicular to PC, however, how can I deduce, by looking at the question intially, that the perpedicular line from A to PC will be on a point halfway of PC, (bisects PC)?
1573146064277.png Are you familiar with vector cross-product?
 

hoosie

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May 30, 2014
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