Find the coordinates of centroid of ΔABC if the mid point of BC is D(2, 4) and vertex A is (2, -3).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\left(2,\displaystyle\frac{5}{3}\right)\)
AD joins vertex A to the midpoint D of the opposite side BC, so AD is a median, and the centroid G lies on it, dividing AD in the ratio 2 : 1 from A. By the section formula, \(\displaystyle G=\frac{1\cdot A+2\cdot D}{3}\).
\(x\)-coordinate \(\displaystyle =\frac{2+2\times2}{3}=\frac{6}{3}=2\)
\(y\)-coordinate \(\displaystyle =\frac{-3+2\times4}{3}=\frac{5}{3}\)
