The line joining two points A(2,0) and B(3,1) | vedclass

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(A) The slope of the line $AB$ is $m = \frac{1-0}{3-2} = 1$. Since $m = 	an 	heta = 1$,the angle of inclination is $	heta = 45^\circ$. When the lin

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$\sqrt{3}x - y - 2\sqrt{3} = 0$

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(A) The slope of the line $AB$ is $m = \frac{1-0}{3-2} = 1$. Since $m = 	an 	heta = 1$,the angle of inclination is $	heta = 45^\circ$. When the line is rotated anti-clockwise about point $A$ by $15^\circ$,the new angle of inclination becomes $	heta' = 45^\circ + 15^\circ = 60^\circ$. The slope of the new line is $m' = 	an 60^\circ = \sqrt{3}$. The line passes through $A(2,0)$,so the equation is given by $y - 0 = \sqrt{3}(x - 2)$. $y = \sqrt{3}x - 2\sqrt{3}$. Rearranging the terms,we get $\sqrt{3}x - y - 2\sqrt{3} = 0$.

The line joining two points $A(2,0)$ and $B(3,1)$ is rotated about $A$ in an anti-clockwise direction through an angle of $15^\circ$. The equation of the line in the new position is:

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