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Centroid from Vertices Worksheets

Find triangle centroids from three given vertices, with exact integer or fraction coordinates.

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Add the three x-values and divide by three; repeat for the y-values.

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Average the coordinates separately

For A(x1, y1), B(x2, y2) and C(x3, y3), the centroid is G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Learning objective

What this activity builds

Find a triangle centroid by averaging its three x-coordinates and three y-coordinates.

Worked example

Find the centroid of A(-3, 0), B(3, 0), and C(0, 3).

G = (0, 1).

The x-coordinate is (-3 + 3 + 0) / 3 = 0. The y-coordinate is (0 + 0 + 3) / 3 = 1.

Teaching notes

Make the practice count

  • Keep x-values and y-values in separate sums.
  • Divide each sum by three, even when a coordinate is zero.
  • Keep thirds as exact fractions instead of rounding.

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Use the three printed ordered pairs. Worked keys preserve exact reduced fractions.

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Math SheetNameScoreTeacherDateCentroid from VerticesFind the centroid G of each triangle. Give exact coordinates as integers or simplified fractions.1.A(-11, -3), B(9, 16), C(2, -16)G =2.A(-17, 8), B(2, 11), C(-9, 13)G =3.A(-14, 12), B(-13, 17), C(-15, -8)G =4.A(5, 3), B(19, -18), C(-17, 7)G =5.A(15, 11), B(5, -20), C(-5, 0)G =6.A(18, -9), B(18, 4), C(7, -11)G =7.A(19, -7), B(9, -13), C(-13, 8)G =8.A(15, -11), B(9, 17), C(15, -7)G =9.A(-9, -17), B(-18, 0), C(9, -19)G =10.A(17, 13), B(-8, 10), C(-8, 20)G =Use exact fractions when needed.math-sheet.comPage 1 of 1

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