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If two vertices of a triangle are (0,2) ...

If two vertices of a triangle are `(0,2)` and `(4,3)` and its orthocentre is `(0,0)` then the third vertex of the triangle lies in (a) `1^(st)` quadrant (b) `2^(nd)`quadrant (c) `3^(rd)`quadrant (d) `4^(th)`quadrant

A

first

B

third

C

fourth

D

second

Text Solution

Verified by Experts

The correct Answer is:
D

`"(Slope)"_(AM)=(2-0)/(0-0)=oo`
`"(Slope)"_(BC)=0` As AM is perpendicular to BC
Equation of BC `rArr (y-3)/(x-4)=0`
`y-3=0`
`y=3`
`"(Slope)"_(BN)=(3-0)/(4-0)=(3)/(4)`
`"(Slope)"_(AC)= -(4)/(3)` (As BN is perpendicular to AC)
Equation of Ac `rArr (y-2)/(x-0)= -(4)/(3)`
`3y-6=-4x rArr 4x+3y=6`
Point of intersection of y=3 and `4x+3y=6`
`4x+9=6`
`4x= -3`
`x= -(3)/(4)" " c=(-(3)/(4),3)`
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