Consider a square with vertices at `(1,1)(-1,1)(-1,-1)and(1,-1).` Let S be the region consisting of all points inside the square which are nearer to the origin than to any edge. Sketch the region S and find its area.

Let R be the region satisfying 'yx-1,x 0, then area of R is

Let C be the chord of a circle S of radius r which subtends angle (2 pi )/(3) at the centre of S. If R represents the region consisting of all points inside S which are closer to C than to the circumference of S, then probability of selecting a point from the region R is.

Show that the points quad (1,7),(4,2),(-1,-1) and (-4,4) are the vertices of a square.

Let O(0,0),A(2,0),a n dB(1 1/(sqrt(3))) be the vertices of a triangle. Let R be the region consisting of all those points P inside O A B which satisfy d(P , O A)lt=min[d(p ,O B),d(P ,A B)] , where d denotes the distance from the point to the corresponding line. Sketch the region R and find its area.

Show that the points P(2,1), Q(-1,3) , R (-5,-3) and S (-2,-5) are the vertices of a square .

Sketch the region bounded by the curves y=sqrt(5-x^(2)) and y=|x-1| and find its area.

Show that the points (-2,4,1),(-1,5,5),(2,2,5) and (1,1,1) are the vertices of a square.

Area of the triangle having vertices (1,2,3),(2,-1,1) and (1,2,4) in square units is

Prove that the points (2, -1), (4, 1), (2, 3) and (0, 1) are the vertices of a square.

Show that the points A(2, 1), B(0,3), C(-2, 1) and D(0, -1) are the vertices of a square.