Locus of Mid-point
Consider two points and If point moves along the line what is the equation of the locus of the mid-point of
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1 solution
Let the midpoint of PQ be expressed as:
((a + a-b)/2, (4a+b + b)/2) = ((2a-b)/2, (4a+2b)/2) (i)
If the point P(a,b) moves according to the line y = -x, then b = -a. Substituting this value into (i) yields:
(3a/2, a)
and we obtain the set of parametric equations:
x = 3a/2, y = a
which results in y = 2x/3 => 2x - 3y = 0.