Question 9.

9. A stick of length 10 units rests against the floor and a wall of a room.
If the stick begins to slide on the floor then the locus of its middle points -
(A) x+ y2 = 2.5
(B) x2 + y2 = 25
(C) x2+ y2 = 100
(D) none

Dear student, 

Let the stick be AB with Aon the wall and B on the floor. Assume that the vertical plane containing the stick is perpendicular to the wall.Let the point on the floor vertically below A be O. Then, AOB = 90°Since, AB= 10 and it has constant length the distance from O to the mid-point M on AB has length 102=5.So, Mlies on a circle center at O.Equation of the circle will be:x2 +y2 = 25

Hence, correct answer for this question will be option (B).


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