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