If the coordinates of two points `A` and `B` are (3, 4) and `(5,-2)` , respectively, find the coordinates of any point `P` if `P A=P Bdot` Area of ` P A B` is 10 sq. units.

Options

A. (2,7)
B. (7,2)
C. (1,0)
D. (0,1)

Answer

B

Explanation

Let the coodinates of P be (x,y). Then,
`PA=PB`
`rArr PA^(2)=PB^(2)`
`rArr (x-3)^(2)+(y-4)^(2)=(x-5)^(2)+(y+2)^(2)`
`x-3y-1=0" "....(i)`
Now,
Area of `DeltaPAB=10`
`rArr(1)/(2)|{:(x,y,1),(2,4,1),(5,-2,1):}|=+-10`
`rArr 6x+2y-26=+-20 " "....(ii)`
Solving (i) with, equations in (ii), we obtain `x=7,y=2 and x=1,y=0`
But, P does lie on any of the coordinarte axes.
Thus, the coordinates of P are (7,2)