Name:___________________________________
Date:_______ Period:_____
Points of Concurrency: Centroid HW
Ms. Anderle
Points of Concurrency: Centroid
Answer all of the questions below.
1. In ΔRST, medians ̅̅̅̅̅
𝑇𝑀 and ̅̅̅̅
𝑆𝑃 are concurrent at point Q. If TQ = 3x – 1 and QM = x+1,
what is the length of median ̅̅̅̅̅
𝑇𝑀.
̅̅̅̅ , and ̅̅̅̅
2. In ΔABC, points J, K, and L are the midpoints of sides ̅̅̅̅
𝐴𝐵 , 𝐵𝐶
𝐴𝐶 , respectively. If
the three medians of the triangle intersect at point P and the length of ̅̅̅̅
𝐿𝑃 is 6, what is
̅̅̅̅?
the length of median 𝐵𝐿
̅̅̅̅ , 𝐶𝐹
̅̅̅̅ is the median to ̅̅̅̅
̅̅̅̅ is the
3. In triangle ACE, ̅̅̅̅
𝐸𝐷 is the median to 𝐴𝐶
𝐴𝐸 and 𝐴𝐻
median to ̅̅̅̅
𝐶𝐸 . The medians meet at Q. If AQ = 24, find the measure of ̅̅̅̅
𝐴𝐻 .
Given the coordinates, determine the coordinates of the centroid of each triangle.
4. a. D(0,0), E(3,15), and F(12,0)
b. G(1,0), H(1,6), and I(10,0)
c. Q(-2,0), R(-4,-3), and S(-12,-6)