Intersection of vector and triangle side

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SUMMARY

The discussion focuses on finding the intersection point, p, between a vector originating from vertex A of triangle ABC and side BC. The solution involves determining the coordinate equations for both the vector and line BC, then solving these equations as a pair of simultaneous equations. This method provides a definitive approach to locating the intersection point in a geometric context.

PREREQUISITES
  • Understanding of coordinate geometry
  • Knowledge of simultaneous equations
  • Familiarity with vector representation
  • Basic concepts of triangle geometry
NEXT STEPS
  • Study coordinate geometry techniques for line equations
  • Learn about solving simultaneous equations in two variables
  • Explore vector mathematics and its applications in geometry
  • Investigate properties of triangles and their vertices
USEFUL FOR

Students studying geometry, mathematicians interested in vector applications, and educators teaching coordinate systems and triangle properties.

virusys
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Homework Statement



I have a triangle with given vertices ABC. Given a vector that starts from A and intersects side BC, how can I find the point of intersection, p?

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Thanks


Homework Equations





The Attempt at a Solution

 
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welcome to pf!

hi virusys! welcome to pf! :smile:

find the two coordinate equations of the red line and of the line BC, and solve them as a pair of simultaneous equations :wink:
 

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