## 2.3. Centroid of Three Points A, B, and C

We are now going to construct the centroid of three points by entering the following lines in the input field and pressing the Enter key at the end of each line. Of course, you can also use the mouse to do this construction using the corresponding modes (see Modes) in the toolbar.

A = (-2, 1)

B = (5, 0)

C = (0, 5)

M_a = Midpoint[B, C]

M_b = Midpoint[A, C]

s_a = Line[A, M_a]

s_b = Line[B, M_b]

S = Intersect[s_a, s_b]

Alternatively you can compute the centroid directly as S1 = (A + B + C) / 3 and compare both results using the command Relation[S, S1].

Subsequently we can experiment whether S = S1 is true for other positions of A, B, and C as well. We do this by selecting mode Move with the mouse and dragging the points.

Related Topics

2. Examples

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