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
In ΔABC if the mid point of BC is D(2, 4) and vertex A is (2, -3)
Given A = (2,-3) is a vertex of the triangle. D is mid-point of the base.
Hence AD is median of the triangle. As per the property of a triangle, the centroid G is such that AG = 2 DG.
That is to say G divides AD in the ratio of 1 : 2
Let ( a , b ) be the coordinates of thr point G. Then—
a = [ 1 * 2 + 2 *(2) ] divided by 3 = 6/3 = 2
b = [ 1 (-3) + 2 (4) ] divided by 3 = 5/3
The correct answer is Option (4) → $(2,\frac{5}{3})$