Find a point within a triangle such that the sum of the square of its distances...

Find a point within a triangle such that the sum of the square of its distances from the three angular points is a minimum.

Solutions

Expert Solution

Procedure of finding the point:

1. First find out the two variable distance function considering a locus point P(x,y) and adding the squares of distance of point P to each of the vertices.

2. We thendthen the critical points of the distance function by equating fx =0 and fy =0.

3. Then we use the second derivative test on the critical points to find out if the point is a local minimum or local maximum.

We know distance between two points =

Incidentally, this point has a particular name which is known as the centroid of the triangle.

milcah answered 1 year ago

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