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Find the coordinates of the orthocentre of the triangle , the equations of whose sides are x+y=2,2x+3y=6,4x-y+4=0 without finding vertices of the triangle.

Find the coordinates of the orthocentre of the triangle , the equations of whose sides are x+y=2,2x+3y=6,4x-y+4=0 without finding vertices of the triangle.

Grade:11

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
5 years ago
x + y = 1
2x + 3y = 6
4x - y = 4

WITHOUT FINDING THE COORDS OF ITS VERTICES!!!

one way is take teh famiily of straight lines passing through the two lines of the triangle..

THen find the condition that they are perpendicular to the third line by seeing the slope..

In the same way find the equation of the second perpendicular..

SOlve them to get the equation of the Orthocenter

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