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if algebric sum of distances of a variable line from points (2,0),(0,2),(-2,-2) is zero,then the line passes through which fixed point?

if algebric sum of distances of a variable line from points (2,0),(0,2),(-2,-2) is zero,then the line passes through which fixed point?

Grade:12

1 Answers

Vikas TU
14149 Points
10 years ago

Let the eqn. of the variable line be y = mx +c

 

1) distance from point (2,0) is given by:

      a1 = mod[(2m + c)/underroot(m^2 + 1)]

2)  distance from point (0,2) is given by:

      a2 = mod[(-2 + c)/underroot(m^2 + 1)]

3) distance from point (-2,-2) is given by:

      a3 = mod[(-2m + 2 +c)/underroot(m^2 + 1)]

 

Now, a1 + a2 + a3 = 0

=>            mod[(2m + c)/underroot(m^2 + 1)] + mod[(-2 + c)/underroot(m^2 + 1)] +      mod[(-2m + 2 +c)/underroot(m^2 + 1)] = 0

=> 2m + c -2 +c - 2m + 2 +c = 0

=> 3c = 0

=> c = 0

 

Therefore, it proves that the line has its intercepts 0 .i.e the line is passing through the fixed point Origin <--------------> (0,0)

 

plz approve!

plz approve!

plz approve!

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