Statement-1 : The point is the mirror image of the point in the line .Statement-2 : The line bisects the line segment joining and .
- AStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
- BStatement-1 is true, Statement-2 is false.
- CStatement-1 is false, Statement-2 is true.
- DStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
Solution & Step-by-step Explanation
Midpoint of : .Check if lies on the line:, , .Since and the -coordinates match (), lies on the line. Statement 2 is true.For Statement 1 to be true, must also be perpendicular to the line.Direction vector of : .Direction vector of line: .Dot product: .Since they are perpendicular and the midpoint lies on the line, is the mirror image of .Statement 2 is true but bisecting is only one condition (perpendicularity is the other). However, in standard AIEEE logic, if both are true and S2 is a necessary condition, it's often linked. Let's verify standard answer: the perpendicular bisector is the definition of a mirror.