Area (in sq units) enclosed by y = 1, 2x + y = 2 and x + y = 2

If algebraic sum of distances of a variable line from points (2, 0), (0,and (-2, -is zero, then the line passes through the fixed point

If C is the reflection of A(2,in X - axis and B is the reflection of C is Y - axis, then |AB| is equal to

Point Q is symmetric to P(4, -with respect to the bisector of the first quadrant. The length of PQ is

One possible condition for the three points (a, b), (b, a) and (a², - b²) to be collinear, is

If points (5,, (10,k) and (-5,are collinear , then k =

The mid point of the line joining the points (-10,and (-6,divides the line joining the points (4, -and (-2,in the ratio

The image of the center of the circles x² + y² = a² with respect to the mirror image x + y = 1 is

If P(1, 2), Q (4, 6), R(5,and S (a, b) are the vertices of a parallelogram PQRS, then

The point P is equidistant from A (1, 3), B (-3,and C (5, - 1), then PA is equal to

The mid - points of the sides of a triangle are D (6, 1), E (3,and F(-1, - 2), then the vertex opposite to D is

(0, -and (0,are two opposite vertices of a square. The other two vertices are

Points (1/2, - (13/4)) divides the line joining the points (3, -and (-7,in the ratio of

The ratio in which the line x + y = 4 divides the line joining the points (1, -and (5,is

The circumcentre of the triangle with vertices (8, 6), (8, -and (2, -is at the point

ABC is a triangle with vertices A(-1,, B(6, -and C (-2, 4), D, E and F are the points which divide each AB, BC and CA, respectively in the ratio 3 : 1 internally. Then, the centroid of the ∆DEF is

The vertices of a triangle are A (0, 0), B (0,and C (2, 0), then find the distance between its orthocentre and circumcentre

Orthocentre of the triangle formed by the lines x - y = 0, x + y = 0, x = 3, is

Three distinct points A, B and C' given in the two-dimensional coordinate plane such that the ratio of the distance of any one of them from the point (1,to the distance from the point (-1,is equal to 1/ 3. Then, the circumcentre of the .ABC is at the point

The vertices of a triangle are (6, 0), (0,and (6, 6). The distance between its circumcentre and centroid is

The coordinates of the incentre of the triangle having sides 3x - 4y = 0, 5x + 12y = 0 and y - 15 = 0 are

The orthocentre of the triangle with vertices O (0, 0), A (0, 3/2), B (-5,is

The centroid if the ∆ABC, where A = (2,, B = (8,and C = (5,is

The circumcentre of the triangle with vertices (0, 30), (4,and (30,is

The coordinates of the orthocentre of the triangle formed by (0,, (8,and (4,is

The vertices P, Q and R of a triangle are (2,, (5,and (3, 4), respectively. Then, the circumcentre is

In ∆ABC ,G is the centroid, D is the mid-point of BC. If A = ( 2,3 ) and G = ( 7,5 ), then the point D is

Let ABC be a triangle, two of whose vertices are (15,and (0, 10). If the orthocentre is (6, 9), then the third vertex is

If orthocentre and circumeentre of a triangle are respectively (1,) and (3. 2), then the coordinates of its centroid are