Question

Statement-1: The point $A(1,0,7)$ is the mirror image of the point $B(1,6,3)$ in the line $:\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$.
Statement-2: The line: $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ bisects the line segment joining $A(1,0,7)$ and $B(1,6,3)$.

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

Answer 1

Answer: (C)

The mid point of $A(1,0,7)$ and $B(1,6,3)$ is (1,3,5)
which lies on the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$
Also the line passing through the points $A$ and $B$ is perpendicular to the given line, hence $B$ is the mirror image of $A,$ consequently the statement- 1 is true.
Statement- 2 is also true but it is not a correct explanation of statement- 1 as there are infinitely many lines passing through the midpoint of the line segment and one of the lines is perpendicular bisector.