If the two vertices of a triangle are (5, 4), and (-2, 4) and the centroid is (5, 6), then the third vertex is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (12, 10)
The centroid of a triangle is the point where its medians meet, and its coordinates are the averages of the coordinates of the three vertices: \(\left(\frac{x_1+x_2+x_3}{3},\ \frac{y_1+y_2+y_3}{3}\right)\). Each coordinate of the third vertex \((x, y)\) is found separately.
\(x\)-coordinate: \(\displaystyle \frac{5+(-2)+x}{3}=5\), so \(3+x=15\) and \(x=12\)
\(y\)-coordinate: \(\displaystyle \frac{4+4+y}{3}=6\), so \(8+y=18\) and \(y=10\)