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ICSE Class 10 Answered

The line x-4y=6 is perpendicular bisector of line AB. If B=(1,3);find coordinates of A  
Asked by Aviral | 05 Feb, 2019, 10:37: PM
answered-by-expert Expert Answer
Line x-4y = 6 is perpendicular to line AB.
 
Hence equation of line AB is of the form : 4x+y = k .
 
Since the coordinate of B is (1,3) , we have   4(1)+3 = k   or k = 7
 
Equation of AB is 4x+y = 7
 
Coordinate of point of intersection is obtained by solving the equations of line AB and that of its perpendicular bisector.
 
x -4y = 6 ....................(1)
4x+y = 7  .......................(2)
 
By solving eqn.(1) and (2), we get x = 2, y = -1
 
if coordinate of A is ( xA , yA ) , we have  (xA + 1)/2  = 2   and (yA + 3)/2 = -1  or  xA = 3 and yA = -5
 
hence coordinate of A is (3, -5)
Answered by Thiyagarajan K | 06 Feb, 2019, 07:12: AM

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