Find the equation of the locus of the third vertex of a triangle if two of its vertices are (1, -2) and (5, 0) and whose area is 3.
Use Determinant method ,
A= =3
x(-2-0)-y(1-5)+(0-(-10)=
-2x+4y+10=
Hence 4y= 2x-10+6 or 4y= 2x-10-6
that is , 4y = 2x -4 or 4y = 2x -16
y=1/2x-1 or y= 1/2x-4.
and the required locus is any point on either of these lines.
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