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Answer:
The equations of the cross roads where the elephant is standing are
x- y+2=0 ……… A
y- 1=o. …………B that is y= 1
putting y= 1 in equation A we get x-1+2=0 or x= (-)1
Therefore the co ordinates of the junction where elephant is standing is (-)1, 1.
Given the equation of the road where the elephant wants to go is x - y-3=0 or y = x-3.
The shortest distance of a point to a given line is the perpendicular distance of the point to the given line. The slope of a line perpendicular to a given line will be equal to the negative reciprocal of the given line. That is if the slope of a line is “m “, then the slope of the line perpendicular to this line will be “(-1/m)”.
Equation of the line representing the road where the elephant wants to go is y=x-3.Its slope = 1.
Therefore the slope of the line perpendicular to the above line is (-)1.Therfore the general equation of the perpendicular is y= - x +k, where ‘k” is a constant …….C .
Now the junction (where the elephant is standing) is a point on the perpendicular whose co ordinates we have found as (-)1 , 1.Therfore this point should satisfy the equation of the perpendicular. Putting these values in equation “C” ,we get 1= -{ (-)1} +k = 1+k which gives the value of k=0.
Therefore the equation of the perpendicular is y= - x+0 or x +y=0.
Equation of the path to be followed by the elephant is x+ y=0
Answer: Option (i)
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