First slide

Equation of line in Straight lines

Question

Let B(1,-3) and D (0,4) represents two $∠ B A D = 60^{0}$ can be equal to

Moderate

A

$(\frac{1 - 7 \sqrt{3}}{2}, \frac{1 - \sqrt{3}}{2})$
B

$(\frac{1 + 7 \sqrt{3}}{2}, \frac{1 + \sqrt{3}}{2})$
C

$(\frac{- 1 + 7 \sqrt{3}}{2}, \frac{- 1 + \sqrt{3}}{2})$
D

$(\frac{- 1 - 7 \sqrt{3}}{2}, \frac{- 1 - \sqrt{3}}{2})$

Solution

$B = (1, - 3), D = (0, 4), P (1 / 2, 1 / 2)$
$\tan θ = \frac{1}{7}, \sin θ = \frac{1}{5 \sqrt{2}}, \cos θ = \frac{7}{5 \sqrt{2}}$
$A P = \frac{5}{2} \sqrt{2} \cot 30^{0} = \frac{5}{2} \sqrt{2} \sqrt{3}$
$A = (\frac{1}{2} \pm A P \cos θ, \frac{1}{2} \pm A P \sin θ)$

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