Question

Statement-I: The point $A(3,1,6)$ is the mirror image of the point $B(1,3,4)$ in the plane $x-y+z=5$.
Statement-2: The plane $x-y+z=5$ bisects the line segment joining $A(3,1,6)$ and $B(1,3,4)$.

• A. (1 ) StatementI is true. Statement-1 is true: Statement--2 is a correct explanation for Statement-1.
• B. (2) StatementI is true, Statement-2 is true: Statement-9 is not a correct explanation for statement-1.
• C. (3) Statement--I is true, Statement-2 is false.
• D. (4) StatementI is false. Statement-2 is true.

Answer 1

The correct option is A (1 ) StatementI is true. Statement-1 is true: Statement--2 is a correct explanation for Statement-1.

Mid-point of AB=$\begin{array}{c}=\left(\frac{3+1}{2},\frac{1+3}{2},\frac{4+6}{2}\right)\\ =(2,2,5)\end{array}$
lies on the plane as it satisfies the equation of the plane
and DR s of AB $=(2,-2,2)$
DR s of normal to the plane $=(1,-1,1)$
AB is the perpendicular bisector.
Hence, A is the image of 2