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NCERT Class XI Mathematics - Straight Lines - Solutions

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Question : 23 of 74
Marks: +1, -0
The vertices of ΔPQR are P(2, 1), Q(–2, 3) and R(4, 5). Find equation of the median through the vertex R.
Solution:  
The vertices of ΔPQR are P(2, 1), Q(–2, 3) and R(4, 5).
Let S be the midpoint of PQ.
So, S = (−2+22,3+12)\left(\frac{-2+2}{2},\frac{3+1}{2}\right) = (0, 2)
Equation of median RS is y−5x−4\frac{y-5}{x-4} = 2−50−4\frac{2-5}{0-4}
⇒ y−5x−4\frac{y-5}{x-4} = −3−4\frac{-3}{-4} ⇒ 4y - 20 = 3x - 12
⇒ 3x – 4y + 8 = 0 is the required equation.
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