Question

Statement 1: If $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ be the images of point $P(x,y)$ about lines $L_1\equiv ax+by+c$ and $L_2\equiv bx-ay+c^{\prime }=0$ respectively, then the line joining points $P_1$ and $P_2$ always passes through point of intersection of lines $L_1$ and $L_2$
Statement 2: Lines $L_1$ and $L_2$ are perpendicular

• A. Statement $1$ is true, statement $2$ is also true; statement $2$ is the correct explanation of statement $1$
• B. Statement $1$ is true, statement $2$ is also true; statement $2$ is not the correct explanation of statement $1$
• C. Statement $1$ is true, statement $2$ is false
• D. Statement $1$ is false, statement $2$ is true

Answer 1

The correct option is A Statement $1$ is true, statement $2$ is also true; statement $2$ is the correct explanation of statement $1$

$\because L_1\perp L_2$ form $m_1{m}_2=-1$


Then from the figure, $\theta +\varphi ={90}^{\circ }$
Let the line joining $P_1$ and $P_2$ pass through intersection of $L_1$ and $L_2$ which is true as $L_1$ and $L_2$ are perpendicular. (because perpendicular bisector of right angle triangle meet at hypotenuse)
$\therefore$ Both the statements are true and statement $2$ is correct explanation of statement $1$.