Question

Lines $L1$ and $L2$ are perpendicular that intersect at the point $(2,3)$. If $L1$ passes through the point $(0,2)$, then line $L2$ must pass through the point

• A. $(0,3)$
• B. $(1,1)$
• C. $(3,1)$
• D. $(5,0)$
• E. $(6,7)$

Answer 1

The correct option is C $(3,1)$

Given that:

Point of intersection of $L_1$ and $L_2$ is $(2,3)$

and $L_1$ passes through $(0,2)$

Solution:

Equation of the line $L_1:$

$y-2=\frac{3-2}{2-0}(x-0)$

or, $2y-4=x$

or, $y=\frac{x}{2}+2$

Since, $L_1$ and $L_2$ are perpendicular.

$m_1{m}_2=-1$

or, $\frac{1}{2}\times m_2=-1$

or, $m_2=-2$

Equation of line $L_2:$

$y-3=-2(x-2)$

or, $y-3=-2x+4$

or, $2x+y=7$

Only $(3,1)$ satisfies the equation of $L_2$

Hence, C is the correct option.