A1A2A3, …. An are points in a plane whose coordinates are (x1y1), (x2y2), (x3y3) …, (xnyn) respectively

A1Ais dissected at the point G1GA3 is divided in the ratio  1 : 2 at G2GA4 is divided in the ratio 1 : 4 at G4, and so on until all n points are exhausted. The coordinates of the final point G so obtained are


Correct option is

The coordinates of G1 are


Now, G2 divides G1A3 in the ratio 1: 2. Therefore, the coordinates of G2are



Again, G3 divides G2A4 in the ratio 1: 3. Therefore, the coordinates ofG2 are    



Proceeding in this manner, we can show that the coordinates of the final point G so obtained will be




If three vertices of a rectangular are (0, 0), (a, 0) and (0, b), length of each diagonal is 5 and the perimeter 14, then the area of the rectangle is


If the line joining the points A(a2, 1) and B(b2, 1) is divides in the ratio b : a at the pint P whose x-coordinate is 7, their


If two vertices of a triangle are (3, –5) and (–7, 8) and centroid lies at the pint (–1, 1), third vertex of the triangle is at the point (a, b) then


α is root of the equation x2 – 5x + 6 = 0 and β is a root of the equation x2– x – 30 = 0, then coordinates  of the point P farthest from the origin are


 are two points whose mid-point is at the origin.  is a point on the plane whose distance from the origin is


Locus of the point P(2t2 + 2, 4t + 3), where t is a variable is


If the coordinates of An are (n, n2) and the ordinate of the center of mean position of the points A1A2, … An is 46, then n is equal to


Area of the triangle with vertices A(3, 7), B(–5, 2) and C(2, 5) is denoted by Δ. If ΔA, ΔBΔC denote the areas of the triangle with vertices OBC, AOC and ABO respectively, O being the origin, then


If the axes are turned through 450. Find the transformed from the equation

                          3x2 + 3y2 + 2xy = 2


If x1 = ay1 = bx1x­2 …. xn and y1y2 …. yn from an ascending arithmetic progressing with common difference 2 abd 4 respectively, then the coordinates of G are