JEE Advance - Mathematics (1983 - No. 56)
The coordinates of $$A, B, C$$ are $$(6, 3), (-3, 5), (4, -2)$$ respectively, and $$P$$ is any point $$(x, y)$$. Show that the ratio of the area of the triangles $$\Delta $$ $$PBC$$ and $$\Delta $$$$ABC$$ is $$\left| {{{x + y - 2} \over 7}} \right|$$
The problem asks to prove a relationship between the areas of two triangles, PBC and ABC, given the coordinates of their vertices.
The problem asks to find the area of triangle ABC.
The problem asks to find the coordinates of point P such that the area of triangle PBC is half the area of triangle ABC.
The problem asks to find the equation of a line passing through points A and B.
The problem asks to find the distance between points A and C.