A vertex of an equilateral triangle is (2, 3) | vedclass

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(B) The slope of the given side $x + y = 2$ is $m_1 = -1$,which corresponds to an angle of inclination $	heta = 135^\circ$.Since the triangle is equi

Vedclass · Accepted Answer

$y - 3 = (2 - \sqrt{3})(x - 2)$

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(B) The slope of the given side $x + y = 2$ is $m_1 = -1$,which corresponds to an angle of inclination $	heta = 135^\circ$.Since the triangle is equilateral,the other two sides make an angle of $60^\circ$ with the base.The slopes of the other two sides are given by $m = 	an(135^\circ \pm 60^\circ)$.For the first case,$m = 	an(135^\circ - 60^\circ) = 	an(75^\circ) = 2 + \sqrt{3}$.For the second case,$m = 	an(135^\circ + 60^\circ) = 	an(195^\circ) = 	an(15^\circ) = 2 - \sqrt{3}$.Using the point-slope form $y - y_1 = m(x - x_1)$ with the vertex $(2, 3)$,the equations are $y - 3 = (2 \pm \sqrt{3})(x - 2)$.Thus,one of the equations is $y - 3 = (2 - \sqrt{3})(x - 2)$.

$A$ vertex of an equilateral triangle is $(2, 3)$ and the equation of the opposite side is $x + y = 2$. Then,the equation of one of the other two sides is:

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