Question

The ortho centre of the triangle with vertices $(-2,-6),(-2,4)$ and $(1,3)$ is

• A. $(3,1)$
• B. $(1,1/3)$
• C. $(1,3)$
• D. None of these

Answer 1

Answer: (C)

Let the vertices of the triangle are
$A(-2,-6),B(-2,4)$ and $C(1,3)$
Now, $AB=\sqrt{(-2+2{)}^2+(-6-4{)}^2}=10$
$BC=\sqrt{(-2-1{)}^2+(4-3{)}^2}=\sqrt{10}$ and
$CA=\sqrt{(1+2{)}^2+(3+6{)}^2}=\sqrt{90}$
Here, $A{B}^2=B{C}^2+C{A}^2$
$\therefore$ Triangle is right angled triangle at $C$.
$\therefore$ $\angle C=90^{\circ }$ So, orthocenter is $(1,3)$.