Question

Assertion :The point $A(1,0,7)$ is the mirror image of the point $B(1,6,3)$ in the line : $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ Reason: 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. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Mid-point of AB is $M(1,3,5)$

M lies on the line

Directions ratios of AB is $<0,6,-4>$

Direction ratios of given line is $<1,2,3>$

As AB is perpendicular to the line

$\therefore 0.1+6.2+4.3=0$

Hence, both assertion and reason are correct but the reason is not the correct explanation for the assertion.