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
The correct answer is Option (4) → (−4, −15)
The centroid is the average of the three vertices: each of its coordinates is the sum of the vertices' coordinates divided by 3.
Assuming the third vertex to be \((x, y)\):
\(\displaystyle\frac{-1+5+x}{3}=0\), so \(4+x=0\) and \(x=-4\)
\(\displaystyle\frac{4+2+y}{3}=-3\), so \(6+y=-9\) and \(y=-15\)
The third vertex is (−4, −15).