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  • The vertices of ∆ PQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

Q : 9 The vertices of  \Delta \hspace{1mm}PQR are  P(2,1),Q(-2,3)  and   R(4,5). Find equation of the median through the vertex R. 

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The vertices of  \Delta \hspace{1mm}PQR are  P(2,1),Q(-2,3)  and   R(4,5)
Let m be RM b the median through vertex R
Coordinates of M (x, y ) = \left ( \frac{2-2}{2},\frac{1+3}{2} \right )= (0,2)
Now, slope of line RM
m = \frac{y_2-y_1}{x_2-x_1} = \frac{5-2}{4-0}= \frac{3}{4}
Now, equation of line passing through point (x_1,y_1) and with slope m is
(y-y_1)= m(x-x_1)
equation of line passing through point (0 , 2) and with slope \frac{3}{4} is
(y-2)= \frac{3}{4}(x-0)\\ \\ 4(y-2)=3x\\ 4y-8=3x\\ 3x-4y+8=0
Therefore, equation of median is 3x-4y+8=0

Posted by

Gautam harsolia

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