Question

If A(3,-5),B(10,-2),C(x,y)forms a triangle and G(2,-1) is its centroid,find the coordinates of 'c '

Answer 1

Formula

Centroid of ΔABC is mean value of x, y coordinates of A, B, C.

$\frac{3+10+x}{3} =2$

$x+13=6$

∴$x=-7$

$\frac{-5-2+y}{3} =-1$

$y-7=-3$

∴$y=4$

∴$C(-7,4)$

Answer 2

The coordinates of C is  ( -7, 4).

Step-by-step explanation:

Given,

The three vertices of Δ ABC = A(3, -5), B (10, -2) and C(x, y)

The centroid of the Δ ABC =G(2, - 1)

To find, the co-ordinate of C(x, y) = ?

We know that,

The co-ordinate of G

$=(\dfrac{x_{1}+x_{2}+x_{3}}{3}, \dfrac{y_{1}+y_{2}+y_{3}}{3})$

∴ $\dfrac{3+10+x}{3}$= 2

⇒ 13 + x = 6

⇒ x = 6 - 13 = - 7

And,

$\dfrac{-5-2+y}{3}$ = - 1

⇒ - 7 + y = - 3

⇒  y = - 3 + 7 = 4

∴ The coordinates of C = ( -7, 4)

Thus, the coordinates of C is  ( -7, 4).