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Triangle Inequality Theorem: The sum of the lengths of two sides of a triangle is less than the third side.
The optimal point for the refinery would be (4.72, 5.72) becuae when the equations connecting points B and D, and C and A intersect and create the point (4.72, 5.72).
coordinates: A (1,2) B (3,8) C(6,7) D (6,4) Intersection point: (4.72,5.72) A to C y: 1x =plus =1 B to D y: -1.33x+++ plus 12
In Part 1e., oil rig B being relfelcted across the shoreline. We intersected the connection of oil rig B to its reflection across the shoreline and the shoreline. This gave us the shorest distance for the refinery to be located.
By finding the equation for lines connecting points AC and BD then finding their intersecting point, by pressing 2nd, trace,5 then enter 3 times in your calculator, after entering the equations in your calculator. The Triangle Inequality Theorem was used when finding the intersecting point of line BD and line AC because it is a shorter distance for all pipleines to connect at a common point instead of traveling around because according to the theorem : b plus c is greater than a.
The Triangle Inequality Theorem is shown in Part 1e. becuase it was a shorter distance to go from oil rig B to the shoreline rather than go from oil rig B to oil rig A then to the shoreline.
