Two vertices of a triangle are (-1, 4) and (5, 2) and its centroid is (0, -3). Find its third vertex.

(-4, -15)

Let us consider that 3rd point is C(a , b)

Then the coordinates of centroid are,

G = \(\frac{ -1 + 5 + a }{ 3 }\) , \(\frac{ 4 + 2 + b }{ 3 }\)

According to question  centroid is G (0 , -3)

0 = \(\frac{ -1 + 5 + a }{ 3 }\)  &  -3 = \(\frac{ 4 + 2 + b }{ 3 }\)

a = -4 & -9 = 6 + b

a = -4 & b = -15

So, Third vertex is ( -4 , -15 )

The correct answer is Option (4) → (-4, -15)