If `p,x_1,x_2,x_3....` and `q,y_1,y_2,y_3,...` from two infinite AP's with common difference `a` and `b` respectively. Then locus of `p(alpha,beta)` where `alpha=(1/n)[x_1+x_2+x_3+...+x_n]` and `beta=(1/n)[y_1+y_2+y_3+...y_n]` is

If a,x_(1), x_(2), x_(3) …..and b, y_(1), y_(2) , …..form two infinite A.P's with common difference p and q respectively then the locus of P(h, k) when h=(x_(1)+x_(2)+x_(3)……+x_(n))/(n) , k=(y_(1)+y_(2)+……..+y_(n))/(n) is

If a,x_1,x_2,.... and b,y_1,y_2... form two infinite G.P's with same common ratio 'r' then the locus of P(h,k) when h= (x_1x_2x_3...x_n)^(1/n) and k=(y_1y_2y_3.....y_n)^(1/n) is

p,x_(1), x_(2) ,. . . x_(n) and q, y_(1),y_(2), . . . ,y_(n) are two arithmetic progressions with common differences a and b respectively. If alpha and beta are the arithmetic means of x_(1), x_(2), . . . . X_(n), and y_(1), y_(2), . . . . Y_(n) respectivley . then the locus of p(alpha, beta) is

p,x_(1), x_(2) ,. . . x_(n) and q, y_(1),y_(2), . . . ,y_(n) are two arithmetic progressions with common differences a and b respectively. If alpha and beta are the arithmetic means of x_(1), x_(2), . . . . x_(n), and y_(1), y_(2), . . . . y_(n) respectivley . then the locus of p(alpha, beta) is

If a, x_1, x_2, …, x_k and b, y_1, y_2, …, y_k from two A. Ps with common differences m and n respectively, the the locus of point (x, y) , where x= (sum_(i=1)^k x_i)/k and y= (sum_(i=1)^k yi)/k is: (A) (x-a) m = (y-b)n (B) (x-m) a= (y-n) b (C) (x-n) a= (y-m) b (D) (x-a) n= (y-b)m

If x_(1),x_(2),x_(3) as well as y_(1),y_(2),y_(3) are in A.P. with the same common difference , then show that the points (x_(1),y_(1)),(x_(2),y_(2))and(x_(3),y_(3)) are collinear.

If x_1, x_2 , x_3 and y_1 , y_2 , y_3 are both in G.P. with the same common ratio, then the points (x_1 , y_1),(x_2 , y_2) and (x_3 , y_3)

If x_(1),x_(2),x_(3), are in A.P.and y_(1),y_(2),y_(3), are also in A.P.with same common difference then the points (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) form