Q. Orthocentre of the triangle formed by the lines $x + y = 1$ and $xy = 0$ is
A) $(0,\ 0)$
B) $(0,\ 1)$
C) $(1,\ 0)$
D) $( - 1,\ 1)$
Explanation
(a)
We have, $x + y = 1$ …(i)
and $xy = 0$ …(ii)
[image:10_image3.emf]
On putting $x = 1 - y$ from Eq. (i) into Eq. (ii), we get
$(1 - y)y = 0$
$\Rightarrow y = 0,\ 1$
At $y = 0 \Rightarrow x = 1$
and at $y = 1\ \Rightarrow x = 0$
$\therefore$ Coordinates of the vertices of a triangle are (0, 0), (1, 0) and (0, 1)
$\therefore$ Point (0, 0) is its orthocentre
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.