1.

A and B are the two points (3,4) and (5,-2). Find the point P such that PA=PB and area of triangle PAB =10 square units.

Answer»

SOLUTION

Here, P=P(X,y) be the required point.

Then,

=) PA= PB= PA^2= PB^2

= > (x - 3) {}^{2} + (y - 4) {}^{2} = {( x - <klux>5</klux>)}^{2} + {(y + 2)}^{2}

=) x-3y-1= 0.............(1)

Again,

Area of ∆PAB=10

=)1/2[x(4+2)+3(-2-y)+5(y-4)]=10

=) 3x+y-23=0.............(2)

On solving (1) &(2), we get

=) x= 7 and y= 2

Hence, the required POINTS (7,2).

hope it helps ✔️


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