1. Tardigrade
  2. Question
  3. Mathematics
  4. Statement-1: The point A(1,0,7) is the mirror image of the point B(1,6,3) in the line: (x/1)=(y-1/2)=(z-2/3). Statement-2: The line: (x/1)=(y-1/2)=(z-2/3) bisects the line segment joining A(1,0,7) and B(1,6,3).

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Q. 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 $B(1,6,3)$.

AIEEEAIEEE 2011Three Dimensional Geometry

Solution:

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.