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Question

Which one of the following points on the line 2x - 3y = 5 is equidistant from (1, 2) and (3, 4)?

A
(7, 3)
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B
(4, 1)
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C
(1, -1)
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D
(-2, -3)
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Solution

The correct option is B (4, 1)
Let point P(x1,y1) be equidistant from point A(1, 2) and B(3, 4).
PA = PB
PA2=PB2
(1x1)2+(2y1)2=(3x1)2+(4y1)21+x212x1+4+y214y1=9+x216x1+16+y218y1x1+y1=5
As P(x1,y1) lies on 2x - 3y = 5
2x13y1=5
On solving Eqs. (1) and (2), we get
x1=4 and y1=1
Coordinates of P are (4, 1).

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