Question 9 9 A stick of length 10 units rests against the floor and a wall of - Maths - Straight Lines

Question

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) x2 + y2 = 2 5
(B) x2 + y2 = 25
(C) x2+ y2 = 100
(D) none

Mayank Jha · Accepted Answer

Dear student,

Let the stick be AB with A on 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, M lies 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)

Regards

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) x2 + y2 = 2.5 (B) x2 + y2 = 25 (C) x2+ y2 = 100 (D) none

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) x²+ y² = 2.5
(B) x² + y² = 25
(C) x²+ y² = 100
(D) none