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

Answer 1

Answer: (B)

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

The direction ratio of the line segment joining points $A(1,0,7)$ and $B(1,6,3)$ is $0,6,-4$.
The direction ratio of the given line is $1,2,3$.
Clearly $1.0+2.6+3.(-4)=0$
So, the given line is perpendicular to line $AB$.
Also , the mid point of $A$ and $B$ is $(1,3,5)$ which lies on the given line.
So, the image of $B$ in the given line is $A$, because the given line is the perpendicular bisector of line segment joining points $A$ and $B$.
Hence, option 'B' is correct.