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  • Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of D ABC.Find the coordinates of points Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1

7.(iii)   Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of D ABC.Find the coordinates of points   Q and R on medians  BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1

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best_answer

From the figure,

triangle pqr

\Rightarrow The point Q divides the median BE in the ratio, BQ : QE = 2 : 1

Hence using the section formula,

Q(x,y)= \left (\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}} , \frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}} \right )

Q(x,y)= \left (\frac{2\times\frac{5}{2}+1\times6}{2+1} , \frac{2\times3+1\times5}{2+1} \right ) = \left ( \frac{11}{3}, \frac{11}{3} \right )

\Rightarrow The point R divides the median CF in the ratio, CR : RF = 2 : 1

Hence using the section formula,

R(x,y)= \left (\frac{m_{1}x_{2}+m_{2}x_{1}}{m_{1}+m_{2}} , \frac{m_{1}y_{2}+m_{2}y_{1}}{m_{1}+m_{2}} \right )

R(x,y)= \left (\frac{2\times 5+1\times1}{2+1} , \frac{2\times\frac{7}{2}+1\times4}{2+1} \right ) = \left ( \frac{11}{3}, \frac{11}{3} \right )

Posted by

Divya Prakash Singh

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