Trisecting a line segment. Let A(x1, y1) and B(x2, y2) be two points in a coordinate plane...

Trisecting a line segment. Let A(x1, y1) and B(x2, y2) be two points in a coordinate plane.

a. Show that the point  is one-third of the way from A to B.

[Hint: Show that d(A, C) + d(C, B) = d(A, B) and that .]

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b. Show that the point  is two-thirds of the way from A to B.

The points C and D in parts a and b are called the points of trisection of segment AB.

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c. Find the points of trisection of the line segment joining (–1, 2) and (4, 1).