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Geometry/Find Point Perpendicular to Line

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Question
find point D
find point D  
Hey Hussain,

I wanna ask you how to find a point, for example there is straight line from point A to B (AB) and point C could be anywhere, how to find point D (line CD should be perpendicular to line AB), for more understanding please refer to the image.

Thanks

Answer
Hello Fendi,

If you are familiar with vectors, you can find the orthogonal projection of AC on AB, then add that to A to get a vector with the coordinates of D.

Alternatively, if you know that parallel lines have slopes that are negative reciprocals, you can do the following.  Use the coordinates of A and B to obtain an equation for the line AB.  Get the slope of AB.  Use that to get the slope of line CD.  You now have the slope of CD and you know it passes through the point C, so you can obtain the equation of line CD.  Finally, solve the system of equations of lines AB and CD.  The solution will be the point of intersection, that is the coordinates of point D.

Thanks for asking,
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.

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