Question

In $\Delta$$ABC$, side $BC$ has equation $x+2y=3$. Coordinates of vertex $A$ are $(1,2)$. If the $x$-coordinate of the orthocentre of $\Delta ABC$ is $3,$ then the $y$-coordinate of the orthocentre is

• A. $4$
• B. $6$
• C. $8$
• D. $10$

Answer 1

The correct option is B $6$

x-co-ordinate of orthocentre $\Delta ABC$ is $3.$

So, equation of line $\perp$ to BC and passing through point $A(1,2)$ is

$y-2=2(x-1)$......(using m1.m2 = -1 => m2 = 2)

$y-2x=0$

As we know, orthocenter is a intersection of attitudes drawn

from vertex of triangle

So, $(3,y)$ lie on $y-2x=0$

So, $y=2x$

$=2\times 3$

$y=6.$