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The Coordinates of a Point Relative to a Triangle

Let be a triangle with side lengths , , . Let be any point and , , be the algebraic distance from to , , , respectively.
Let and be the Conway triangle parameters for triangle and set the coordinates of the base to be and .
Then the Cartesian coordinates of the other two points are:
,
.
Also,
,
,
.

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 Minh Trinh Xuan
"The Coordinates of a Point Relative to a Triangle"
 http://demonstrations.wolfram.com/TheCoordinatesOfAPointRelativeToATriangle/
 Wolfram Demonstrations Project
 Published: May 12, 2022
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