The line 
= 1 meets the axis of y and axis of x at A and B respectively. A square ABCD is constructed on the line segment AB away from the origin, the coordinates of the vertex of the square farthest from the origin are -
Text Solution
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The coordinates of A are (0, 4) and that of B are (3, 0).
Let CL and DM be perpendiculars on x-axis and
y-axis respectively then if ∠ OBA = θ .
∠ CBL = ∠ ADM = 90° – θ [See figure]
also, BC = AB = 
= 5
⇒ BL = BC sin θ and CL = BC cos θ
⇒ BL = 5 × 
= 4 and CL = 5 × 
= 3
Similarly, MD = 4 and AM = 3.
So the co-ordinates of C are (OB + BL, CL) = (7, 3) and of D are (MD, OA + AM) = (4, 7)
The co-ordinates of the vertex farthest from the origin are therefore (4, 7).
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