SOLUTION: An equilateral triangle has its centroid at origin and one side is on the line x+y=1. Find the equations of other sides.
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Question 984302: An equilateral triangle has its centroid at origin and one side is on the line x+y=1. Find the equations of other sides.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
An equilateral triangle has its centroid at origin and one side is on the line x+y=1. Find the equations of other sides.
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The perpendicular bisector of the given side is y = x
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Then intersection of the bisector and the line x+y = 1 is at (0.5,0.5)
The distance from the centroid to the vertex on y = x is 2x the distance from the origin to the line --> the vertex is at (-1,-1)
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The slope of x+y=1 is -1 --> the tangent of the angle with the x-axis = 135 degs
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The angles of the 2 other sides with the x-axis are 75 degs and 195 degs.
The slope of a line = the tangent of the angle with the x-axis.
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Find the eqns of the lines thru (-1,-1) with slopes of the atan(75) and atan(195).
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= slope
--> y + 1 = (2 - sqrt(3))*(x + 1) ***** eqn of 1 line
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= slope
--> y + 1 = (2 + sqrt(3))*(x + 1) ***** eqn of the other line
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