Let A (a,b) be a fixed point and O be the origin of coordionates. If `A_(1)` is the mid-point of OA, `A_(2)` is the mid- poind of `A A_(1),A_(3)` is the mid-point of ` A A_(2)` and so on. Then the coordinates of `A_(n)` are

Mid point of A(0,0) and B(1024,2048) is At. mid point of A_(1) and B is A_(2) and so on. Coordinates of A_(10) are.

A square S_(1) encloses another square S_(2) in such a manner that each corner of S_(2) is at the mid-point of the side of S_(1). If A_(1) is the area of S_(1) and A_(2) is the area of S_(2), then A_(1)=4backslash A_(2) (b) A_(1)=2backslash A_(2)( c) A_(2)=2backslash A_(1)( d ) A_(1)=A_(2)

A_(1),A_(2)…A_(n) are points on the line y = x lying in the positive quadrant such that OA_(n)=nOA_(n-1), O being the origin. If OA_(1)=1 and the coordinates of A_(n) are (2520sqrt(2), 2520sqrt(2)) , then n =

If O is the origin anf A_(n) is the point with coordinates (n,n+1) then (OA_(1))^(2)+(OA_(2))^(2)+…..+(OA_(7))^(2) is equal to

If A_(1),A_(2),A_(3),…,A_(n) are n points in a plane whose coordinates are (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),…,(x_(n),y_(n)) respectively. A_(1)A_(2) is bisected in the point G_(1) : G_(1)A_(3) is divided at G_(2) in the ratio 1 : 2, G_(2)A_(4) at G_(3) in the1 : 3 and so on untill all the points are exhausted. Show that the coordinates of the final point so obtained are (x_(1)+x_(2)+.....+ x_(n))/(n) and (y_(1)+y_(2)+.....+ y_(n))/(n)

If A_(1),A_(2),A_(3),…,A_(n) are n points in a plane whose coordinates are (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),…,(x_(n),y_(n)) respectively. A_(1)A_(2) is bisected in the point G_(1) : G_(1)A_(3) is divided at G_(2) in the ratio 1 : 2, G_(3)A_(5) at G_(4) in the1 : 4 and so on untill all the points are exhausted. Show that the coordinates of the final point so obtained are (x_(1)+x_(2)+.....+ x_(n))/(n) and (y_(1)+y_(2)+.....+ y_(n))/(n)

If A_(1),A_(2),A_(3),…,A_(n) are n points in a plane whose coordinates are (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),…,(x_(n),y_(n)) respectively. A_(1)A_(2) is bisected in the point G_(1) : G_(1)A_(3) is divided at G_(2) in the ratio 1 : 2, G_(3)A_(5) at G_(4) in the1 : 4 and so on untill all the points are exhausted. Show that the coordinates of the final point so obtained are (x_(1)+x_(2)+.....+ x_(n))/(n) and (y_(1)+y_(2)+.....+ y_(n))/(n)

If A_(1),A_(2)......A_(n) are points on the line y=x lying in the positive quadrant such that OA_(n)=n.OA_(n-1),O being the origin.If OA_(1)=1 then the co-ordinates of A_(8) are (3a sqrt(2),3a sqrt(2),) where a is equal to

Let points A_(1), A_(2) and A_(3) lie on the parabola y^(2)=8x. If triangle A_(1)A_(2)A_(3) is an equilateral triangle and normals at points A_(1), A_(2) and A_(3) on this parabola meet at the point (h, 0). Then the value of h I s

Let points A_(1), A_(2) and A_(3) lie on the parabola y^(2)=8x. If triangle A_(1)A_(2)A_(3) is an equilateral triangle and normals at points A_(1), A_(2) and A_(3) on this parabola meet at the point (h, 0). Then the value of h I s