# A triangle ABC is formed by three lines x + y +2 = 0, x - 2y + 5 = 0 and 7x + y - 10 = 0. P is a point inside the triangle ABC such that areas of the triangles PAB, PBC, and PCA are equal?

##
If the co-ordinates of the point P are (a,b) and the area of the triangle ABC is D, then find (a + b + D).

If the co-ordinates of the point P are (a,b) and the area of the triangle ABC is D, then find (a + b + D).

##### 1 Answer

#### Explanation:

1) Given three lines

1a) let

1b) Similarly, let

1c) Similarly, let

2) Recall that when the centroid of a triangle is joined to the vertices of a triangle, it divides the triangle into 3 equal areas, and given that areas of

3) Recall that if

Hence