Perpendicular Bisector & Altitude of Triangle: A(4;2) B(11;6) C(-3;-1)

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SUMMARY

The discussion focuses on determining the equations of the perpendicular bisector of side a and the altitude of side c in triangle ABC with vertices A(4,2), B(11,6), and C(-3,-1). The proposed equation for the perpendicular bisector is -7x + 14y = 7, while the altitude's equation is suggested as -4x + 7y = 5. The participants seek clarification on identifying side a and finding the intersection of these two lines.

PREREQUISITES
  • Understanding of triangle geometry, specifically the concepts of perpendicular bisectors and altitudes.
  • Familiarity with coordinate geometry and the Cartesian plane.
  • Knowledge of solving linear equations and finding intersections of lines.
  • Ability to calculate midpoints and slopes of line segments.
NEXT STEPS
  • Learn how to derive the equation of a perpendicular bisector in coordinate geometry.
  • Study the method for calculating the altitude of a triangle from a vertex to the opposite side.
  • Explore techniques for finding the intersection point of two linear equations.
  • Review the properties of triangles, including side lengths and angles, to clarify terminology.
USEFUL FOR

Students studying geometry, mathematics educators, and anyone interested in understanding triangle properties and line equations in coordinate systems.

adod
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The vertices of a triangle are A(4;2) ; B(11;6) ; C(-3;-1)
What is the equation of the perpendicular bisector of side a?
(i think -7x+14y=7)
What is the equation of the altitude of side c?
(i think -4x+7y=5)
What is the intersection of the previous lines?
i have no idea about this,please help,and also write down how you solved it
 
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adod said:
The vertices of a triangle are A(4;2) ; B(11;6) ; C(-3;-1)
What is the equation of the perpendicular bisector of side a?
(i think -7x+14y=7)
What is the equation of the altitude of side c?
(i think -4x+7y=5)
What is the intersection of the previous lines?
i have no idea about this,please help,and also write down how you solved it

Welcome to PH (=
what is side a? AB? AC ? BC?
 
Side a is usually the side across from angle A.

How does one normally find the point of intersection of two lines?
 

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