Statement-1: The point A(1,0,7) is the mirror image of the point B(1,6,3) in the line 1x=2y−1=3z−2.
Statement-2: The line 1x=2y−1=3z−2 bisects the line segment joining A(1,0,7) and B(1,6,3).
Solutions · 1
Official solution
The directions 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.