Key points to solve the problem:

• Idea of distance formula- Distance between two points A(x₁,y₁) and B(x₂,y₂) is given by- AB =

Area of a ΔPQR – Let P(x_1,y₁) , Q(x₂,y₂) and R(x₃,y₃) be the 3 vertices of ΔPQR.

Ar(ΔPQR) =

How to approach: To find the locus of a point we first assume the coordinate of the point to be (h, k) and write a mathematical equation as per the conditions mentioned in the question and finally replace (h, k) with (x, y) to get the locus of the point.

Let the coordinates of a point whose locus is to be determined to be (h, k). Name the moving point to be C

Given the area of ΔABC = 9

According to question:

9 =

⇒ 18=|-10-5k+3k-9+3h+2h|

⇒ |5h-2k-19|=18

∴ 5h-2k-19=18 or 5h-2k-19= -18

⇒ 5h-2k-37=0 or 5h-2k-1=0

Replace (h,k) with (x,y)

Thus, locus of point is 5x-2y-37=0 or 5x-2y-1=0 …….ans