Question

if the co-ordinate of two point A and B are 3, 4 and 5, - 2 respectively find the co-ordinate of any point P if P A equal to PB and area of triangle p a b is equal to 10 square units​

Answer 1

if PA =PB ,then
By distance formula,
under root (x-3)^2 +(y-4)^2 = (x-5)^2 +(y+2)^2
x^2+9 -6x +y^2+16-8y=x^2+25-10x+y^2+4+4y
9-6x+16-8y=25-10x+4+4y
10x-6x-4y-8y=25-9
4x-12y=16
x-3y=4
x=4+3y ............... (i)
Area of triangle pab =10
-6+5y+4x-20+2x-3y=10
6x+2y-26=10
6x+2y=36
3x+y=18 ............. (ii)
putting the value of x in eq. (i)from (ii)
3×(4+3y)+y=18
12+9y+y=18
10y=6
y=6/10
putting the value of y in eq. (i)
x=4+3×6/10
x=40+18/10
x=58/10
x=29/5