The coordinates of points A, B, C and P are `(6, 3), (-3, 5), (4, -2) and (x, y)` respectively, prove that `(DeltaPBC)/ (Delta ABC) = (x+y-2)/7`

The coordinates of points A,B,C and D are (-3, 5), (4, -2), (x, 3x) and (6, 3) respectively and Area of (Delta ABC)/(Delta BCD)=(2)/(3) ,find x.

The coordinates of the points A, B, C are (0, 4), (2, 5) and (3 , 3) respectively. Prove that AB=BC and the angle ABC is a right angle.

The coordinates of A ,\ B ,\ C are (6,\ 3),\ (-3,\ 5) and (4,\ -2) respectively and P is any point (x ,\ y) . Show that the ratio of the areas of triangles P B C and A B C is |(x+y-2)/7| .

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 P B C to that of A B C is (|x+y-2|)/7dot

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 P B C to that of A B C is (|x+y-2|)/7dot

In a triangle, ABC, the equation of the perpendicular bisector of AC is 3x - 2y + 8 = 0 . If the coordinates of the points A and B are (1, -1) & (3, 1) respectively, then the equation of the line BC & the centre of the circum-circle of the triangle ABC will be

If the coordinates of two points A and B are (3,\ 4) and (5,\ -2) respectively. Find the coordinates of any point P , if PA = PB, and area of triangle PAB is 10.

The coordinates of the vertices of a triangle are (4, -3), (-5, 2) and (x, y). If the centroid of the triangle is at the origin, show that x=y=1 .

The base and the altitude of a triangle are (3x - 4y) and (6x + 5y) respectively. Find its area.

The centroid of a triangle ABC is at the point (1, 1, 1) . If the coordinates of A and B are (3, 5, 7) and (1, 7, 6) , respectively, find the coordinates of the point C.