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.

Find the area of the triangle with vertices at (-4,1),(1,2),(4,-3).

Find the square roots : 1-i

Find the area of the with vertices at (a,(1)/(a)),(b,(1)/(b))and(c,(1)/(c)).

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

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.

Prove that the four ponts (1,1,1),(-2,4,1),(-1,5,5) and (2,2,5) are the vertices of a square.

If one side of the square is 2x-y+6=0, then one of the vertices is (2,1) . Find the other sides of the square.

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

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

The area (in square unit ) of the region bounded by the line y= |x-1| and y=3- |x| is -