By Allen Ma, Amber Kuang

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.

image0.png

  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.

    image1.png

    You’re given that SD = 21; therefore,

    image2.png

  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

    image3.png

    The average of the y coordinates is

    image4.png

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