NIMCET 2009 Question Paper with solutions

Question : 4 of 120

Marks: +1, -0

Let A B C be an isosceles triangle with AB = BC. If base B C is parallel to x -axis and

m_{1}, m_{2}

are slopes of medians drawn through the angular points B and C , then

Solution:

From above figure

m_{1}=1 ; m_{2}=-1{/} 2

But

m_{1}m_{2}=-1{/}2

m_{1}+m_{2}=1{/}2

m_{1}^{2}+m_2^2=(m_{1}+m_{2})^{2}-2 m_1m_2=1{/}4+1

m_1^2+m_2^2=5{/}4

(m_{1}-m_{2})^{2}=(m_{1}+m_{2})^{2}-4 m_{1} m_{2}

=1{/} 4-4(-1 {/}2)=\;{1}/{4}+2=9 {/} 4

m_{1}-m_{2}=3{/} 2

So, no option is correct.

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