line segment of length 2L sliding with ends of the axis then the locus of the middle point of the line segment is.
Answers
Given : line segment of length 2L sliding with ends on the axis
To find : locus of the middle point of the line segment
Solution:
Let say point are (x , 0) & ( 0 , y)
Length = 2L
= √(x - 0)² + (0 - y)²
= √x² + y ²
Mid point = (x + 0)/2 , (0 + y)/2
= (x/2 , y /2)
Mid point = h , k
=> h = x/2 & k = y/2
=> x = 2h & y = 2k
√x² + y ² = 2L
=> x² + y² = 4L²
-> (2h)² + (2k)² = 4L²
=> 4h² + 4k² + 4L²
=> h² + k² = L²
h² + k² = L²
or x² + y² = L² is the locus of the middle point of the line segment
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