Statement-1: The point A(3,1,6) is the mirror image of the point B(1,3,4) in the plane x-y…

Question

Statement-1: The point $A(3,1,6)$ is the mirror image of the point $B(1,3,4)$ in the plane $x-y+z=5$.
Statement-2: The plane $x-y+z=5$ bisects the line segment joining $A(3,1,6)$ and $B(1,3,4)$.

Accepted Answer

$$A\left( {3,1,6} \right);\,\,B = \left( {1,3,4} \right)$$

Mid-point of $$AB = \left( {2,2,5} \right)$$ lies on the plane.

and d.r's of $AB=(2,-2,2)$

d.r's of normal to plane $$ = \left( {1, - 1,1} \right).$$

Direction ratio of $AB$ and normal to the plane are proportional therefore,

$AB$ is perpendicular to the plane

$$\therefore$$ $A$ is image of $B$

Statement-$2$ is correct but it is not correct explanation.

Solutions · 1