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

x^{2} +y^{2} – 4x – 2y + 5 = x^{2} +y^{2} – 2x + 4y + 5

2x + 6y = 0

or x + 3y = 0

∴ The correct option is **A**.

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