If (1,p/3)is the mid-point of the line segment joining the points (2, 0) and (0,2/9),then show that the line 5x + 3y + 2 = 0 passes through the point (-1, 3p).
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Step-by-step explanation:
Using mid-point formula, mid point of (2,0) & (0,2/9):
= ( (2+0)/2 , (0+2/9)/2 )
= (1, 1/9)
But in question mid point of the same points is (1,p/3),this means, (1, 1/9) = (1, p/3)
=> 1/9 = p/3
=> 3/9 = p
=> 1/3 = p
Which means, point (-1, 3p) is (-1, 3(1/3)) = (-1, 1).
If (-1, 3p), which is now (-1, 1), lies on 5x + 3y + 2 = 0, then it must satisfy all the conditions of 5x + 3y + 2 = 0. It lies of 5x + 3y + 2 = 0, if 5(1) + 3(-1) + 2 is 0,
=> 5 - 3 + 2
=> 0, it proves the point (1, -1) lies on 5x + 3y + 2 = 0
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