What is the value of m and the coordinates of C?

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1 Answer
Jan 29, 2018

see explanation.

Explanation:

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let m_(AB), m_(AC) and m_(BC) be the slope of AB, AC and BC, respectively.
a) m_(AB)=(4-1)/(-1-1)=-3/2
given m_(AB)=-3m, => -3m=-3/2, => m=1/2
=> m_(AC)=3m=3/2, and m_(BC)=m=1/2

b) let (x,y) be the coordinates of C,
m_(AC)=3/2=(y-1)/(x-1),
=> 3x-2y-1=0 ----- Eq(1)
similarly, m_(BC)=1/2=(y-4)/(x+1),
=> x-2y+9=0 ----- Eq(2)
Eq(1)-Eq(2), => 2x-10=0,
=> x=5, substituting x=5 in Eq(1) or Eq(2), we get,
y=7,
=> coordinates of C=(5,7)