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  • The orthocentre of the triangle formed by  (0, 0), (8, 0), (4, 6) is  Option: 1 <img alt="\mathrm{(4, \frac{8}{3})}" src="https:/

The orthocentre of the triangle formed by  (0, 0), (8, 0), (4, 6) is

 

Option: 1

\mathrm{(4, \frac{8}{3})}


Option: 2

\mathrm{\left ( 3,4 \right )}


Option: 3

\mathrm{(4,3)}


Option: 4

\mathrm{(-3,4)}


Answers (1)

best_answer

Let ABC be the given triangle and the vertices be \mathrm{A}(0,0), \mathrm{B}(8,0) and \mathrm{C}(4,6)

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

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

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

And slope of \mathrm{\mathrm{CA}=(6-0) /(4-0)=\frac{3}{2}}

\mathrm{\therefore } Equation of line through B and ⊥ 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

Divya Prakash Singh

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