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Question: If the co-ordinates of the points A and B be (1, 0) and \(( 2 , \sqrt { 3 } )\), then the angle made...

If the co-ordinates of the points A and B be (1, 0) and (2,3)( 2 , \sqrt { 3 } ), then the angle made by the line AB with x-axis is.

A

30∘30 ^ { \circ }

B

45°

C

60°

D

75°

Answer

60°

Explanation

Solution

Slope of the line is,

tan⁡θ=y2−y1x2−x1=3−02−1\tan \theta = \frac { y _ { 2 } - y _ { 1 } } { x _ { 2 } - x _ { 1 } } = \frac { \sqrt { 3 } - 0 } { 2 - 1 } =3= \sqrt { 3 }⇒ θ=tan⁡−13=60∘\theta = \tan ^ { - 1 } \sqrt { 3 } = 60 ^ { \circ }.