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Question

The orthocentre of a triangle with vertices 0,0,3,4 and 4,0 is


A

3,12

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B

3,34

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C

3,9

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D

None of these

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Solution

The correct option is B

3,34


Explanation for the correct option

Let O0,0,A4,0 and B3,4 be the vertices of the triangle.

Let QB is the perpendicular drawn from the line OA to B

Let PO is the perpendicular drawn from the line AB to O

The intersection of the line QB and PO is the orthocenter of the triangle .

Let H be the point of orthocenter of the triangle ∆OAB

The straight line QB is perpendicular to the x axis and meet B at 3,4

So the co-ordinate of H is 3,y

We know that two lines are perpendicular to each other is the product of their slope is equal to -1

Therefore,

SlopeofOPi.eOH×SlopeofBA=-1⇒y-03-0×4-03-4=-1⇒4y3=1⇒y=34

So, the required orthocentre =3,34

Hence, option B is the correct answer.


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