Question

A(a, 1), B(b, 3) and C(4, c) are the vertices of ΔABC. If its centroid lies on x–axis, then __________.

Answer 1

In ΔABC,
A = (a, 1)
B = (b, 3)
C = (4, c)
Since centroid lies an x-axis
⇒ y-cordinate of centroid is 0

i.e 0 = $\frac{1+3+c}{3}$ (since for A(x₁, y₁) B(x₂, y₂) C(x₃, y₃)
i.e c = –4 (centroid is given by $\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)$