Find the coordinates of centroid of ΔABC if the mid point of BC is D(2, 4) and vertex A is (2, -3).

$(2,\frac{5}{3})$

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) → $(2,\frac{5}{3})$