The figure shows a parallelogram with the coordinates of its vertices: Prove that `x_1+x_3=x_2+x_4andy_1+y_3=y_2+y_4`

What are the coordinates of the centroid of the triangle with vertices (x_1,y_1) (x_2,y_2) and (x_3,y_3)

Let y=3cos(logx)+4sin(logx) Prove that x^2y_2+xy_1+y=0

Write the coordinate 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)

Consider a triangle whose sides are y = x, y = 2x and y = 3x + 4 Find the co-ordinates of the vertices of the triangle.

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y_2-3xy_1-y=0

If y=sin^(-1)x/sqrt(1-x^2) prove that (1-x^2)y_1-xy=1

If x=sint and y=sinmt show that (1-x^2)y_2-xy_1+m^2y=0

If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, |[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4

If the straight lines y=2x ,y=2x + 1, y=-7x and y=-7x +1 form a parallelogram, then the area of the parallelogram (in sq units) is a)1/3 b)2/9 c)1/9d)1/4

The equation of the plane through the line of intersection of the planes x-y+z+3=0 and x+y+2z+1=0 and parallel to x-axis is a) 2y-z=2 b) 2y+z=2 c) 4y+z=4 d) 4y-2z=3