Question
Wed October 03, 2012 By:
 

Find the point on x-axis which is equidistant from A(6,3) and B(-1,4).

Expert Reply
Wed October 03, 2012
Answer : Given : points A(6,3) and B(-1,4)
To find : point on x-axis which is equidistant from A(6,3) and B(-1,4)
 
let the point lying on x axis to be found be given by C (x,0) 
 
as C is equidistant from A and B 
=> AC = BC 
squaring both the sides
=> AC2 = BC2  
using the distance formula ((x2-x1)2 + (y2-y1)2)   { squared of it }
 
=> ( 6 - x )2 + (3-0) = (x-(-1))2 +( 0-4)2
=> 36 + x2 - 12 x + 9 = x2 + 1 + 2x + 16 { using (a-b)2 = a2+b2 -2ab }
 
=> 14x = 28
=> x= 2
therefore the point on x axis required is (2,0) Answer
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