In the xy-coordinate plane, a line segment beginning at the origin and ending at point (a,b ) forms a 30^{\circ} angle with the x-axis. Keeping the starting position at the origin, the angle is increased by 30^{\circ} so that the line segment now ends at point (c,d ).

a and b are positive.

The problem said that after from origin of start it created a 60 degree angle but it never said anything where it stopped at the same half and half ratio of a and b so this seems confusing to me

I apologize to explain the answer. The answer is C (which means equal)

Now the angle lets consider start increasing from origin and till 60 degree but as c refers to x and d refers to y but please suggest me in the question where its told to be reaching till the end? where is it told in the question that the point c,d will create a similar angle with a,b angle with 90 degree and the distance between a,0 and 0,d is supposed to be same

Sketch a diagram. Also what are the two quantities?