Question

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

• A. Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1
• B. Statement-1 is true, Statement-2 is false
• C. Statement-1 is false, Statement-2 is true
• D. Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Answer 1

Answer: (A)

Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation for Statement-1

Answer 2

A(3, 1, 6); B = (1, 3, 4) Mid-point of AB = (2, 2, 5) lies on the plane. and d.r?s of AB = (2, -2, 2) d.r?s Of normal to plane = (1, -1, 1). AB is perpendicular bisector $\therefore$ A is image of B Statement-2 is correct but it is not correct explanation.