Q. 105.0( 2 Votes )
If point (x, y) is at equal distance from points (2, 1) and (1, –2), then the true statement out of the following:
A. x + 3y = 0
B. 3x + y = 0
C. x + 2y = 0
D. 2y + 3x = 0
Answer :
We have A → (2, 1)
B → (1, –2)
P → (x, y)
Using the distance formula,
AP = 
=
=
BP = 
= 
=
=
Since P is equidistant from A and B
∴ AP = BP
=
Squaring both sides, we get
x2 +y2 – 4x – 2y + 5 = x2 +y2 – 2x + 4y + 5
2x + 6y = 0
or x + 3y = 0
∴ The correct option is A.
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