Triangle and orthocentre.

Question

Suppose we have a triangle with vertices $A=(-1,0)$ ,$B=(-2,\frac{3}{4})$ and $C=( -3,-\frac{7}{6})$ Let its orthocentre be $K$ Why does it happen that the orthocentre of triangle $KBC$ comes out to be $A$?

Answer 1

$K$ is the orthocentre of $\triangle ABC$ if and only if $KA\perp BC$, $KB\perp CA$ and $KC\perp AB$.

$A$ is the orthocenter of $\triangle KBC$ if and only if $AK\perp BC$, $AB\perp KC$ and $AC\perp KB$.

Therefore, $K$ is the orthocentre of $\triangle ABC$ if and only if $A$ is the orthocentre of $\triangle KBC$.