Two vertices of a triangle are (-1, 4) and (5, 2) and its centroid is (0, -3). Find its third vertex.
Answer & explanation
Correct answer: option 4
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)