Triangle inequality workshop
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Name: ________________________
Draw a convex quadrilateral ABCD. In this context, convex means that the diagonals of
the quadrilateral intersect at a point, M, inside the figure.
Determine for which point in ABCD the sum of the distances from the point to the
vertices is as small as possible.
Outline:
Choose an arbitrary point, P, inside ABCD. (Sketch)
Use the triangle inequality to compare the sum of the distances from P to the vertices and
the sum of the distances from M to the vertices.
Conclusion …
Can you think of an application for this?
In the super fun game, Math-Tag, you start at point A, run to the line, touch the line at a
single point P, and run to point B. If point A is (11, 5), point B is
(1, 15), and the line is the x-axis, where will you touch the x-axis to make your total trip
as short as possible?
Outline:
Sketch the setup.
What point is just as far from the x-axis as point A? Alternately, from what other point,
A’, will the trip to B be just as far? Think symmetrically.
Once you have the answer, consider how the triangle inequality figures into this.
Can you think of an application for this?