Statement-1 : Only one straight line can be drawn passing through the origin, at equal distances from the points A(2, 2) and B(4, 0). Statement-2 : Only one straight line can be drawn passing through two given points.

Engineering

Mathematics

Family of Straight lines

Question

Statement-1 : Only one straight line can be drawn passing through the origin, at equal distances from the points A(2, 2) and B(4, 0).
Statement-2 : Only one straight line can be drawn passing through two given points.

Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

Statement-1 is false, statement-2 is true.

Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.

Statement-1 is true, statement-2 is false.

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Let y = mx

$∴ |\frac{2 m - 2}{\sqrt{1 + m^{2}}}| = |\frac{4 m}{\sqrt{1 + m^{2}}}|$

∴ 2m – 2 = ± 4m
∴ m = – 1 or m = 1/3

Also slope of AB = – 1
Hence there can be two lines ℓ₁ and ℓ₂ through origin with slopes 1/3 and – 1 which are equidistant from (2, 2) and (4, 0)

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