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 = 0B. 3x + y = 0C. x + 2y = 0D. 2y + 3x = 0

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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