Let L be the line y = 2x , in the two dimensional plane .
Statement 1 : The image of the point (0,1) in L is the point (4/5 , 3/5)
Statement 2 : The points (0,1) and (4/5 , 3/5) lie on opposite sides of the line L and are at equal distance from it .

Options

A. Statement -1 is True , Statement - 2 is true , Statement- 2 is a correct explanation for statement - 15
B. Statement-1 is True , Statement-2 is True , Statement -2 is not a correct explanation for Statement - 1 .
C. Statement-1 is True , Statement - 2 is False .
D. Statement - 1 is False , Statement -2 is True .

Answer

A

Explanation

Given points A(0,1) and B(4/5 , 3/5) are such that the mid-points of AB lies on y =2 x and AB is perpendicular to line y = 2x . So , B is the image of A in the line y = 2x .
For x = 0 , y = 1 , we have
L'` = 2 xx 0 - 1 = 1 lt 0`
For ` x = (4)/(5) , y = (3)/(5)` , we have
`L'' 2 xx (4)/(5) - (3)/(5) = 1 gt 0`
Clearly , L' , L'' `lt ` 0 .So, points A (1,0 ) and B (4/5 , 3/5) are on opposite sides of the line y = 2x .
We observe that (0,1) and (-2 , -5) are equidistant points on the opposite sides of y = 2 x . But , they are not mirror images of each other . So , statement - 2 is not a correct explanation of statement - 1 .