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