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

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

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Answer 1 · 2018-01-29T08:33:45

see explanation.

Explanation:

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let $m_{A B}, m_{A C} and m_{B C}$ $m_(AB), m_(AC) and m_(BC)$ be the slope of $A B, A C and B C$ $AB, AC and BC$ , respectively.
a) $m_{A B} = \frac{4 - 1}{- 1 - 1} = - \frac{3}{2}$ $m_(AB)=(4-1)/(-1-1)=-3/2$
given $m_{A B} = - 3 m, \Rightarrow - 3 m = - \frac{3}{2}, \Rightarrow m = \frac{1}{2}$ $m_(AB)=-3m, => -3m=-3/2, => m=1/2$
$\Rightarrow m_{A C} = 3 m = \frac{3}{2}, and m_{B C} = m = \frac{1}{2}$ $=> m_(AC)=3m=3/2, and m_(BC)=m=1/2$

b) let $(x, y)$ $(x,y)$ be the coordinates of $C$ $C$ ,
$m_{A C} = \frac{3}{2} = \frac{y - 1}{x - 1}$ $m_(AC)=3/2=(y-1)/(x-1)$ ,
$\Rightarrow 3 x - 2 y - 1 = 0 - - - - - E q (1)$ $=> 3x-2y-1=0 ----- Eq(1)$
similarly, $m_{B C} = \frac{1}{2} = \frac{y - 4}{x + 1}$ $m_(BC)=1/2=(y-4)/(x+1)$ ,
$\Rightarrow x - 2 y + 9 = 0 - - - - - E q (2)$ $=> x-2y+9=0 ----- Eq(2)$
$E q (1) - E q (2), \Rightarrow 2 x - 10 = 0$ $Eq(1)-Eq(2), => 2x-10=0$ ,
$\Rightarrow x = 5$ $=> x=5$ , substituting $x = 5$ $x=5$ in Eq(1) or Eq(2), we get,
$y = 7$ $y=7$ ,
$\Rightarrow$ $=>$ coordinates of $C = (5, 7)$ $C=(5,7)$

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

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