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Question

The coordinates of the vertices of a triangle are (0,1),(2,3) and (3,5). Find orthocentre of the triangle.

A
(14,6)
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B
(2,6)
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C
(92,152)
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D
(92,3)
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Solution

The correct option is A (14,6)

Let vertices of triangle be A(0,1),B(2,3) and C(3,5)


And coordinate of orthocentre be H(x,y)


Now slope of AB=3120=1


Then slope of line perpendicular to AB is 1

and mid point of AB is E(1,2)


But slope of HE=y2x1


Equating it with slope of line perpendicular to AB we get


y2x1=1y2=x+1x+y=1 ...(1)


Similarly from BC

y4x52=122y8=x+524y16=2x+52x4y=21 ...(2)


Solving (1) and (2) we get

(x,y)=(14,6)



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