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Q.
Which one of the the following is the nearest point on the line 3x- 4y = 25 from the origin?
Straight Lines
Solution:
Only two point A (-1, - 7) and B (3, 4) satisfy the given equation of the line 3x - 4y = 25
Distance of A (- 1, - 7) from the origin O.
$= \sqrt{\left(0+1\right)^{2}+\left(0+7\right)^{2}} = \sqrt{50} = 5\sqrt{2} $
Distance of B (3, - 4) from the origin O.
$= \sqrt{\left(0-3\right)^{2} + \left(0+4\right)^{2}} = \sqrt{9+16} = \sqrt{25} = 5 $
The nearest point is (3, - 4)