Question

a vertex of an equilateral triangle is (2,3) and the opposite side is x + y = 2 . find the equation of other side​

Answer 1

Answer:

6x-4y=56 is the equation

Answer 2

Answer:

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Step-by-step explanation:

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

Given equation of one side of triangle is x + y = 2 Clearly , point A does not lie on it, hence given equation of line BC.

Slope of line BC = -1

SInce it is equilateral the angle between the sides will be 60°.

Let the slope of the other side be m

=> | m - (-1)|/ 1 +(-1)m = tan 60° = √3

=> |m + 1|/(1-m) = √3

=> m + 1 = ±√3(1 - m)

=> m(√3 + 1) = √3 - 1 or m(√3 -1) = 1 + √3

=> m = (√3 - 1)/(√3 + 1) or (√3 + 1)/(√3 - 1).

Hence the equation of other sides of triangle are

y - 3 = (√3 - 1)/(√3 + 1) (x - 2) and

y - 3 = (√3 + 1)/(√3 - 1) (x - 2)