If `x_1,x_2,x_3` as well as `y_1, y_2, y_3` are in G.P. with same common ratio, then prove that the points `(x_1, y_1),(x_2,y_2),a n d(x_3, y_3)` are collinear.

If x_1,x_2,x_3 as well as y_1,y_2,y_3 are in G P with the same common ratio, then the points (x_1,y_1),(x_2,y_2), and (x_3, y_3)dot (a)lie on a straight line (b)lie on an ellipse (c)lie on a circle (d) are the vertices of a triangle.

If x_(1), x_(2), x_(3) as well as y_(1), y_(2), y_(3) are in GP, with the same common ratio, then the points (x_(1),y_(1)), (x_(2),y_(2)) and (x_(3), y_(3))

Write the condition of collinearity of points (x_1,\ y_1),\ \ (x_2,\ y_2) and (x_3,\ y_3) .

Write the formula for the area of the triangle having its vertices at (x_1,\ y_1),\ \ (x_2,\ y_2) and (x_3,\ y_3) .

.The equation of the circle passing through three non-collinear points P( x_1,y_1 ) Q( x_2,y_2 ) and R( x_3,y_3 ) is

A (3,4 ), B (-3, 0) and C (7, -4) are the vertices of a triangle. Show that the line joining the mid-points D (x_1, y_1), E (x_2, y_2) and F (x, y) are collinear. Prove that (x-x_1) (y_2 - y_1) = (x_2 - x_1) (y-y_1)

Find the coordinates of the centroid of the triangle whose vertices are (x_1,y_1,z_1) , (x_2,y_2,z_2) and (x_3,y_3,z_3) .

If the points A (x,y),(-1,3)and(5,-3) ar collinear, then show that x + y = 2.

y=x^3-2x+1,y=2x+1 The graphs in the system of equations shown above have three points of intersection . (x_1,y_1), (x_2,y_2) and (x_3,y_3) . Find the product x_1 .x_2 .x_3 .

If a, x_(1), x_(2) are in G.P. With common ratio 'r' and b,y_(1),y_(2) are in G.P with common ratio 's' where s-r = 2 then find the area of triangle with vertices (a,b), (x_(1),y_(1)) "and" (x_(2),y_(2)) .