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

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| .

Consider A(2,3,4),B(4,3,2) and C(5,2,-1) be any three points. Find the area of triangle ABC.

Points A, B and C lie on the parabola y^2= 4ax . The tangents to the parabola at A, B and C, taken in pair, intersect at points P, Q and R. Determine the ratio of the areas of the triangles ABC and PQR.

If three points A,B and C have position vectors (1,x,3),(3,4,7) and (y,-2,-5), respectively and if they are collinear, then find (x,y).

A variable plane which is at a constant 6 p from the origin meets the axes in A,B and C respectively. Show that the locus of the centroid of the triangle ABC is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(4p^(2))

If the points A(x_1,y_1), B(x_2,y_2) and C(x_3,y_3) are collinear, then area of triangle ABC is:

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.

If the plane x/2+y/3+z/4=1 cuts the coordinate axes in A, B,C, then the area of triangle ABC is

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to 2 (b) 2/3 (c) 1/3 (d) 3

The combined equation of three sides of a triangle is (x^2-y^2)(2x+3y-6)=0 . If (-2,a) is an interior point and (b ,1) is an exterior point of the triangle, then