If `sum_(i-1)^4(xi2+y i2)lt=2x_1x_3+2x_2x_4+2y_2y_3+2y_1y_4,` the points `(x_1, y_1),(x_2,y_2),(x_3, y_3),(x_4,y_4)` are the vertices of a rectangle collinear the vertices of a trapezium none of these

If three point A(x_(1), y_(1)), B(x_(2), y_(2)) and C(x_(3), y_(3)) will be collinear then the area of triangleABC= ____.

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

A(6,1), B(8,2) and C(9,4) are three vertices of a parallelograam ABCd taken in order. Find the fourth vertex D. IF (x_(1),y_(1)), (x_(2),y_(2)), (x_(3),y_(3)) and (x_(4),y_(4)) are the four vertices of the parallelgraam then using the given points, find the value of (x_(1)+x_(3)-x_(2),y_(1)+y_(3)+y_(2)) and state the reason for your result.

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 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 the points (x_1, y_1),(x_2,y_2), and (x_3, y_3) are collinear show that (y_2-y_3)/(x_2x_3)+(y_3-y_1)/(x_3x_1)+(y_1-y_2)/(x_1x_2)=0

If (x_1-x_2)^2+(y_1-y_2)^2=a^2 , (x_2-x_3)^2+(y_2-y_3)^2=b^2 , (x_3-x_1)^2+(y_3-y_1)^2=c^2 , and k|[x_1,y_1, 1],[x_2,y_2, 1],[x_3,y_3, 1]|=(a+b+c)(b+c-b)(c+a-b)xx(a+b-c) , then the value of k is 1 b. 2 c. 4 d. none of these

If |(3x+4y,-3),(2,x+2y)|=|(7,-3),(2,3)| then x and y are

2x-3y=4,3y-x=4