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  • The orthocentre of the triangle formed by  (0,0), (8,0), (4,6) isOption: 1 (4,8/3)Option

The orthocentre of the triangle formed by 

(0,0), (8,0), (4,6) is

Option: 1

(4,8/3)


Option: 2

(3,4)


Option: 3

(4,3)


Option: 4

(-3,4)


Answers (1)

best_answer

a

Let ABC be the given triangle and the vertices be A(0,0), B(8,0), and C(4,6).

\mathrm{\square} slope of BC=(6,0)/ (4-8) = -3/2.

\mathrm{\therefore }  Equation of line through A and \mathrm{\perp } to BC is

\mathrm{y-0=(2 / 3)(x-0) \text { i.e. } 2 x-3 y=0}(1)

And slope of CA=(6-0)/(4-0)=3/2

\mathrm{\therefore }  Equation of line through B and \mathrm{\perp} to CA is

\mathrm{\begin{aligned} & \quad y-0=(-2 / 3)(x-8) \\ & \text { i.e. } 2 x+3 y=16 . \end{aligned}} (2)

Solving (1) and (2), the orthocentre is (4,8/3),

Which is given in (a).

Posted by

Pankaj Sanodiya

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