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  • The point R divides the line segment AB, where A(– 4, 0) and B(0, 6) such that Find the coordinates of R.  

The point R divides the line segment AB, where A(– 4, 0) and B(0, 6) such that AR= \frac{3}{4}AB. Find the coordinates of R.

 

 
 
 
 
 

Answers (1)

Given
        \frac{AR}{AB}= \frac{3}{4}         
\Rightarrow \frac{AB}{AR}= \frac{4}{3}\Rightarrow \frac{AR+BR}{AR}= \frac{4}{3}
\Rightarrow 1+\frac{BR}{AR}= \frac{4}{3}\; \; \Rightarrow \frac{BR}{AR}= \frac{1}{3}
\Rightarrow AR:BR= 3:1
                                m :  n
Coordinates of R(x,y) = \left ( \frac{mx_{2}+nx_{1}}{m+n},\frac{my_{2}+ny_{1}}{m+n} \right )
                                  = \left ( \frac{3\times 10+1\times 1-4}{1+3},\frac{3\times 6+1\times 0}{1+3} \right )
                                 = \left ( \frac{-4}{4},\frac{18}{4} \right )
R\left ( x,y \right )= \left ( -1,\frac{9}{2} \right )

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Safeer PP

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