Question

Find the equation of the locus of a point which forms a triangle of area 2with a points a1,1 b-2,3

Answer 1

Step-by-step explanation:

The given points of triangle A$\equiv$(1, 1) and B$\equiv$(-2, 3)

Let another point be C$\equiv$(h, k)

Now, we have,

$ar(\triangle ABC)=2$

$\implies1(3 - k) - 2(k - 1) + h(1 - 3) = 2$

$\implies3 - k - 2k + 2 - 2h = 0$

$\implies - 2h - 3k + 5 = 0$

$\implies2h + 3k - 5 = 0$

Hence, the required locus is 2x + 3y - 5 = 0