Question

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

• A. $\left(\frac{9}{4},-\frac{1}{3}\right)$
• B. $\left(4,13\right)$
• C. $\left(4,\frac{9}{4}\right)$
• D. $\left(4,\frac{7}{4}\right)$

Answer 1

Answer: (D)

Consider the triangle with the given information,

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 $\left(4,\frac{7}{4}\right)$