Statement - 1 : If the perpendicular bisector of the line segment joining points A (a,3) and B( 1,4) has y-intercept -4 , then `a = pm 4`.
Statement- 2 : Locus of a point equidistant from two given points is the perpendicular bisector of the line joining the given points .

Options

A. Statement -1 is True , Statement - 2 is true , Statement- 2 is a correct explanation for statement - 3
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

Statement-2 is true . Using statement -2 , the equation of the perpendicular bisector of A (a,3) and B (1,4) is given by
`sqrt((x-a)^(2) + (y-3)^(2)) = sqrt((x -1)^(2) + (y-4)^(2))`
`implies 2 (a + 1) x - 2y = a^(2) - 8`.
This has y-intercept -4 . So , it passes through (0,-4) .
`therefore a^(2) - 8 = 8 implies a = pm 4`
Hence , statement-1 is true . Also , statement -2 is a correct explanation for statement - 1.