Question
Statement-1: The point $$A\left( {1,\,0,\,7} \right)$$ is the mirror image of the point $$B\left( {1,\,6,\,3} \right)$$ 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 $$A\left( {1,\,0,\,7} \right)$$ and $$B\left( {1,\,6,\,3} \right).$$
A.
Statement-1 is true, Statement-2 is true ; Statement-2 is not a 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 a correct explanation for Statement-1.
Answer :
Statement-1 is true, Statement-2 is true ; Statement-2 is not a correct explanation for Statement-1.
Solution :
The direction ratios of the line segment joining points
$$A\left( {1,\,0,\,7} \right)$$ and $$B\left( {1,\,6,\,3} \right)$$ are $$0,\, 6,\,-4.$$
The direction ratios of the given line are $$1, \,2, \,3.$$
Clearly $$1 \times 0 + 2 \times 6 + 3 \times \left( { - 4} \right) = 0$$
So, the given line is perpendicular to line $$AB.$$
Also , the mid point of $$A$$ and $$B$$ is $$\left( {1,\,3,\,5} \right)$$ 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 $$B,$$ But statement-2 is not a correct explanation for statement-1.