Q. If a vertex of a triangle is (1, 1) and the mid points of two sides through this vertex ate (-1, 2) and (3, 2), then the centroid of die triangle is:
AIEEEAIEEE 2005Straight Lines
Solution:
If $A(x_1, y_1),\, B(x_2, y_2)$ and $C(x_3, y_3)$ are the vertices of a triangle, then the co-ordinates of the centroid will be
$\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right).$
Let D and E are mid points of AB and AC. So co-ordinates of B and C are $(- 3, 3)$ and $(5, 3)$ respectively.
Centroid of triangle
$= \left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)$
$= \left(\frac{1-3+5}{3}, \frac{1+3+3}{3}\right)$
$= \left(1, \frac{7}{3}\right)$
