Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)
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In geometry, the centroid of a triangle is the point where the medians intersect. The following practice questions ask you to find the coordinates of a centroid in a triangle and to find the distance from one of the vertices to the centroid, given the median length.

Practice questions

Use the given information to solve the practice questions.

  1. Point C represents the centroid of triangle RST. If SD = 21, find SC.

  2. The vertices of a triangle are (0, –2), (4, 0), and (2, 8). Find the coordinates of the centroid of the triangle.

Answers and explanations

  1. 14

    The centroid of a triangle divides each median of the triangle into segments with a 2:1 ratio. You don't know the length of either segment of the median, so you'll use an x in the ratio to represent the shorter length.


    You're given that SD = 21; therefore,

  2. (2, 2)

    You find the centroid of a triangle by averaging the x coordinates and the y­coordinates of all three vertices of the triangle. The average of the x coordinates is


    The average of the y coordinates is


    Therefore, the centroid of the triangle is (2, 2).

About This Article

This article is from the book:

About the book authors:

Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, New York. Allen, who has taught geometry for 20 years, is the math team coach and a former honors math research coordinator. Amber has taught all levels of mathematics, from algebra to calculus, for the past 14 years.

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