Geometry: An Interactive Journey to Mastery

Lesson 11: Making Use of Linear Equations

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    Part I
    D௘ͽ )LQGWKHFRRUGLQDWHVRIWKHPLGSRLQWM of AB and the equation of the line through M and C.
    E௘ͽ )LQGWKHFRRUGLQDWHVRIWKHPLGSRLQWN of BC and the equation of the line through N and A.
    F௘ͽ )LQGWKHFRRUGLQDWHVRIWKHPLGSRLQWR of AC and the equation of the line through R and B.
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    Part II
    D௘ͽ )LQGWKHHTXDWLRQRIWKHOLQHWKURXJKM and perpendicular to AB.
    E௘ͽ )LQGWKHHTXDWLRQRIWKHOLQHWKURXJKN and perpendicular to BC.
    F௘ͽ )LQGWKHHTXDWLRQRIWKHOLQHWKURXJKR and perpendicular to AC.
    G௘ͽ 6KRZWKDWDOOWKUHHOLQHVSDVVWKURXJKWKHVDPHSRLQWͼ௘௘ͽ
    Part III
    D௘ͽ )LQGWKHHTXDWLRQRIWKHOLQHWKURXJKC and perpendicular to AB.
    E௘ͽ )LQGWKHHTXDWLRQRIWKHOLQHWKURXJKA and perpendicular to BC.
    F௘ͽ )LQGWKHHTXDWLRQRIWKHOLQHWKURXJKB and perpendicular to AC.
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    Comment: Part I of this question constructs the three medians of a triangle, part II constructs the three
    perpendicular bisectors of a triangle, and part III constructs the three altitudes of a triangle. You can use
    algebraic methods to prove that each set of three lines do always pass through a common point for any given
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