Consider Three Points               ,                and               , Then

If a vertex of a triangle is (1, 1) and the mid-point of two sides through the vertex are (–1, 2) and (3, 2), then the centroid of the triangle is

If the equation of the locus of a point equidistant from the points

(a₁, b₁) and (a₂, b₂) is (a₁ – a₁)x + (b₁  –  b₂)y + c = 0,

Then the value of c is :

The line joining the point  is produced to the point L(x, y) so that AL : LB = b : a, then 

The vertex of a triangle are the points A(–36, 7), B(20, 7) and C(0, –8), If G and I be the centoid and in center of the triangle, then GI is equal to

If a, b, c are relation by 4a² + 9b² – 9c² + 12ab = 0 then the greatest distance between any two lines of the family of lines

ax + by + c = 0 is:

Triangle is formed by the coordinates (0, 0), (0, 21) and (21, 0). Find the numbers of integral coordinates strictly inside the triangle (integral coordinates of both x and y)

If x₁, x₂, x₃ as well as y₁, y₂, y₃ are in G.P. with the same common ratio, then the points (x₁, y₁), (x₂, y₂) and (x₃, y₃)

Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

If a, b, c are all unequal and different from one and the points  are collinear then ab + bc + ca =

The lines p(p² + 1)x – y + q = 0 and (p² + 1)² x + (p² + 1)y + 2q = 0 are perpendicular to a common line for