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  4. The orthocentre of the triangle whose vertices are (1,1),(5,1) and (4,5) is

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Q. The orthocentre of the triangle whose vertices are $\left(1,1\right),\left(5,1\right)$ and $\left(4,5\right)$ is

NTA AbhyasNTA Abhyas 2020Straight Lines

Solution:

Consider the triangle with the given information,
Solution
The slope of $AB=0$ , so the equation of altitude from $C$ is $x=4$
The slope of $BC=-4$ , so the equation of altitude from $A$ is $x-4y+3=0$
Solving these two equations, we get,
orthocentre of the triangle is $\left(4 , \frac{7}{4}\right)$