The orthocentre of a triangle formed by the lines x - 2y = 1, x = 0 and 2x + y = 0 is

Question

The orthocentre of a triangle formed by the lines x - 2y = 1, x = 0 and 2x + y = 0 is (A) (0, 1) (B) (1, 0) (C) (-1 ,-2 ) (D) (1, 2)

Tardigrade Admin · Accepted Answer

Given equations of lines are x-2 y=1, x=0 and 2 x+y-2=0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/84c737d62f7a5594cbf759d8741bdef9-.png" /> From figure, Since, AB is perpendicular to AC. So, orthocentre is the meeting point of A B and AC, i.e., (1,0)

Q. The orthocentre of a triangle formed by the lines $x - 2 y = 1, x = 0$ and $2 x + y = 0$ is

(0, 1)

(1, 0)

(-1 ,-2 )

(1, 2)

(0, 0)

Given equations of lines are
$x - 2 y = 1, x = 0$ and $2 x + y - 2 = 0$

From figure,
Since, $A B$ is perpendicular to $A C$ .
So, orthocentre is the meeting point of $A B$ and AC, i.e., $(1, 0)$

Q. The orthocentre of a triangle formed by the lines x−2y=1,x=0 and 2x+y=0 is