Question

the centroid of a triangle ABC is (3,2) if A(2,3) B(3,-1) find the value of C. *

Answer 1

Questions :

the centroid of a triangle ABC is (3,2) if A(2,3) B(3,-1) find the value of C.

Formula :

Centroid of triangle having vertices $\tt ({x}_{1},{y}_{1}) , ({x}_{2},{y}_{2}) \:and\:({x}_{3},{y}_{3})$

(x,y) = $\tt (\frac{{x}_{1}+{x}_{2}+{x}_{3}}{3} , \frac{{y}_{1},{y}_{2},{y}_{3}}{3})$

Solution :

A(2,3) and B(3,-1)

Centroid of triangle is (3,2)

Let the coordinates of C be (x,y)

$\tt (3,2) = (\frac{2+3+x}{3},\frac{3-1+y}{3})$

Comparing x-coordinates

$\implies$ 3 = $\tt \frac{5+x}{3}$

$\implies$ 9 = 5 + x

$\implies$ x = 9 - 5

$\implies$ x = 4

Comparing y-coordinate

$\tt 2 = \frac{2+y}{3}$

$\implies$ 6 = 2 + y

$\implies$ y = 6 - 2

$\implies$ y = 4

The value of C is (4,4)