The coordinates of a b and c are (6,3),(-3,5) and (4,-2) resp.p is a point x,yshow that area of triangle pbc/area of triangle ABC= x+z-2/7

Dear Pavan

Hello Nashwa, area of A(6,3), B(-3,5) and C(4,-2) will be
1/2 * {6(5+2) -3(-2-3)+4(3-5)} = 1/2 * (42 + 15 - 8) = 1/2 * 49 sq units
Now area of triangle PBC with (x,y) (-3,5) (4,-2) will be
1/2 * {x(5+2) -3(-2-y)+4(y-5)} = 1/2 * (7x + 7y - 14) = 7/2 * (x+y-2) sq units
Hence area ? PBC / area ? ABC = 7/2 * (x + y - 2) / 49/2
So required ratio = (x + y - 2) / 7 ]proved]

Regards
Arun (askIITians forum expert)