If a, b and c are in A.P. a, x, b are in G.P. whereas b, y and c are also in G.P.

Show that : x², b², y² are in A.P.

If x, y and z are in G.P., show that x⁴, y⁴ and z⁴ are also in G.P.

Find the values of m and n, in each case; if :

(i) (4, -3) on reflection in x-axis gives (-m, n).

(ii) (m, 5) on reflection in y-axis gives (-5, n - 2)

(iii) (-6, n + 2) on reflection in origin gives (m + 3, -4).

Points A and B have the coordinates (-2, 4) and (-4, 1) respectively. Find :

(i) the co-ordinates of A', the image of A in the line x = 0.

(ii) the coordinates of B', the image of B in the y-axis.

(iii) the coordinates of A", the image of A in the line BB'.

Hence, write the angle between the lines A'A" and BB'. Assign a special name to the figure B'A'BA".