If P(2,-1), Q (3,4), R(-2,3) and S (-3,-2) are four points in a plane, show that PQRS is a rhombus but not a square.

If P(2,\ -1),\ \ Q(3,\ 4),\ \ R(-2,\ 3) and S(-3,\ -2) be four points in a plane, show that P Q R S is a rhombus but not a square. Find the area of the rhombus.

For points P -= (x_(1) ,y_(1)) and Q = (x_(2),y_(2)) of the coordinate plane , a new distance d (P,Q) is defined by d(P,Q) = |x_(1)-x_(2)|+|y_(1)-y_(2)| . Let O -= (0,0) ,A -= (1,2), B -= (2,3) and C-= (4,3) are four fixed points on x-y plane Let S(x,y) such that S is equidistant from points O and B with respect to new distance and if x ge 2 and 0 le y lt 3 then locus of S is

Plot point P(1, 0), Q (4,0) and S(1, 3) . Find the coordinates of R so that PQRS is a square.

Let P(2,-1,4) and Q(4,3,2) are two points and as point R on PQ is such that 3PQ=5QR , then the coordinates of R are

If P(-5,\ -3),\ Q(-4,\ -6),\ R(2,\ -3) and S(1,\ 2) are the vertices of a quadrilateral P Q R S , find its area.

If P(z_(1)),Q(z_(2)),R(z_(3)) " and " S(z_(4)) are four complex numbers representing the vertices of a rhombus taken in order on the complex plane, which one of the following is held good?

If the points P,Q,R,S are (4,7,8),(-1,-2,1),(2,3,4) and (1,2,5) respectively show that PQ and RS intersect. Also find the point of intersection.

If P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4) are four concyclic points on the rectangular hyperbola ) and xy = c^2 , then coordinates of the orthocentre ofthe triangle PQR is

If P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3) and S(x_4,y_4) are four concyclic points on the rectangular hyperbola ) and xy = c^2 , then coordinates of the orthocentre ofthe triangle PQR is

P(2,1) , Q (4,-1) , R (3,2) are the vertices of a triangle and if through P and R lines parallel to opposite sides are drawn to intersect in S , then the area of PQRS , is