Question

The equation of line passing through (1, 1) and making an angle of 60° with positive direction of x-axis is

Answer 1

The passing points are $\large{ \: (\:\underbrace{\red{1}}_{x_1} \: ,\underbrace{\red{1}}_{y_1} \: )}$

Angle (θ) = 60°

Slope (m) :-

• tan θ = tan 60° → √3

Equation of line :-

$\: \: \: \: \: \: \rm{y - y_{1} = m(x - x_{1})} \\ \: \: \: \: \: \rm{y - 1 = \sqrt{3}(x - 1) } \\ \: \: \: \sf{y - 1 = \sqrt{3}x - \sqrt{3} } \\ \: \: \: \: \: \hookrightarrow \boxed{\underline{\rm{y - \sqrt{3}x - 1 + \sqrt{3} = 0 }}}$

Hence, $\rm{y - \sqrt{3}x - 1 + \sqrt{3} = 0 }$is the equation of line.

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Formula used :-

• Slope (m) = tan θ

[ for finding slope ]

• $\rm{y - y_{1} = m(x - x_{1})}$

[ for finding equation of line ]