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  • Point A lies on the line segment XY joining X(6, – 6) and Y(– 4, – 1) in such a way that 

Point A lies on the line segment XY joining X(6, – 6) and Y(– 4, – 1) in such a way that \frac{XA}{XY} = \frac{2}{5}. If point A also lies on the line 3x + k (y + 1) = 0, find the value of k.

 

 

 
 
 
 
 

Answers (1)

Given 

        \frac{XA}{XY} = \frac{2}{5}

\Rightarrow \frac{XA}{XA + AY} = \frac{2}{5}

\Rightarrow 3XA = 2AY

\Rightarrow \frac{XA}{AY} = \frac{2}{3} \ or \ m_1:m_2 = 2:3

If the coordinates of A is (x,y) then

        x = \frac{m_1x_2 + m_2x_1}{m_1 + m_2}    and    y = \frac{m_1y_2 + m_2y_1}{m_1 + m_2}

Here    (x_1, y_1) = (6,-6)    and     (x_2, y_2) = (-4,-1)

        x = \frac{2\cdot (-4) + 3\cdot 6}{5}    and    y = \frac{2\cdot (-1) + 3\cdot (-6)}{5}

        x = 2    and    y = -4

So, the coordinates of A is (2,-4)

Now, A(2,-4) lies on 3x + k(y+1) = 0

then 

        3x + k(y +1)= 0

\Rightarrow 3\cdot 2 + k(-4 +1)= 0

\Rightarrow k = 2

Posted by

Safeer PP

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