QJEEM14Ma5135: JEE Main 2014 Mathematics - Class 11 JEEM14Ma5135 Solution: Let be the median of the triangle with vertices , and . The…

Question

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Let

PS

be the median of the triangle with vertices

P(2, 2)

,

Q(6, -1)

and

R(7, 3)

. The equation of the line passing through

(1, -1)

band parallel to PS is :

Accepted Answer

Let

P,Q,R,

be the vertices of

\Delta PQR

Since

PS

is the median,

S

is mid-point of

QR

So,

S = \left( {{{7 + 6} \over 2},{{3 - 1} \over 2}} \right) = \left( {{{13} \over 2},1} \right)

Now, slope of

PS

= {{2 - 1} \over {2 - {{13} \over 2}}} = - {2 \over 9}

Since, required line is parallel to

PS

therefore slope of required line

=

slope of

PS

Now, equation of line passing through

(1, -1)

and having slope

- {2 \over 9}

is

y - \left( { - 1} \right) = - {2 \over 9}\left( {x - 1} \right)

9y + 9 = - 2x + 2

\Rightarrow 2x + 9y + 7 = 0

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