In triangle ABC, if the orthocenter is (3,−2) and the circumcenter is (0,4), find the centroid.
Show answer & explanation
Correct answer: C
Explanation
Given:
Orthocentre H = (3, −2)
Circumcentre O = (0, 4)
The centroid (G) lies on the Euler line connecting the circumcentre and the orthocentre, and
OG : GH = 1 : 2
G = O + 1/3(H − O)
= (0, 4) + 1/3[(3, −2) − (0, 4)]
= (0, 4) + 1/3(3, −6)
= (0, 4) + (1, −2)
= (1, 2)