Question

                 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

Solution

Correct option is

The coordinates of G1 are

    

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

    

or 

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

    

or 

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

       

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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Q6

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

Q7

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

Q8

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

Q9

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

                          3x2 + 3y2 + 2xy = 2

Q10

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