Let R be a rectangle given by the lines x = 0 , x = 2 , y = 0 and y = 5 . Let A α , 0 and B 0 , β , α ∈ 0 , 2 and β ∈ 0 , 5 , be such that the line segment A B divides the area of the rectangle R in the ratio 4 : 1 . Then, the mid-point of A B lies on a

Step-by-step solution

Given, R be a rectangle given by the lines x = 0 ,   x = 2 , y = 0 and y = 5 And point A α , 0 and B 0 , β ,   α ∈ 0 , 2 and β ∈ 0 , 5 , Now plotting the diagram we get, Now given that line segment A B divides the ratio of area in 4 : 1 , we get 10 - 1 2 α β 1 2 α β = 4 1 ⇒ 20 - α β = 4 α β ⇒ α β = 4   . . . . . . 1 Now using midpoint formula we get, h = α 2   &   β = k 2 Now using eq