If the vertices of a \(\Delta ABC\) are \(A(1, 3), B(3, 5)\) and \(C(x, y)\) and centroid is \(\left(\frac{11}{3},\frac{16}{3}\right)\), then \((x, y)\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (7, 8)
The centroid of a triangle is the point where its medians meet; its coordinates are the averages of the coordinates of the three vertices, \(\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)\).
\(x\)-coordinate: \(\displaystyle \frac{1+3+x}{3}=\frac{11}{3}\)
\(4+x=11\), so \(x=7\)
\(y\)-coordinate: \(\displaystyle \frac{3+5+y}{3}=\frac{16}{3}\)
\(8+y=16\), so \(y=8\)
Each coordinate gives one equation in one unknown, so C is (7, 8).