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# Geometry/Differentiate Points

Question

point
Dear Hussain,

Sorry for the last question, I tried to make it simple question. My question is, if I have polygon with five points and one straight line across the polygon, how to differentiate or populate the points of polygon that exist at one side of the line and another side of the line, please refer to picture for more understanding.

Thanks,

Fendi

Dear Fendi,

This can be done readily if you have the equation of the line and the coordinates of the vertices.  For the sake of illustration, let us suppose the line's equation is y=-x, or x+y=0.  Then, for any point (x,y) calculate x+y (add the two coordinates).  If the result is zero, the point lies on the line.  If the result is greater than 0, the point lies above the line.  If the result is less than zero, the point lies below the line.
This procedure can be generalized to any line and any point.

Azeem

Geometry

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#### Azeem Hussain

##### Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

##### Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.