Answer:
[tex]G(0, -\dfrac{2}{3})[/tex]
Step-by-step explanation:
Given that:
The coordinates of the vertices of a triangle [tex]\triangle PQR[/tex] are given as:
[tex]P(-4, -1)[/tex], [tex]Q(2, 2)[/tex], and [tex]R(2, - 3)[/tex].
To find:
The coordinates of the centroid of the triangle.
Solution:
The coordinates of the centroid of a triangle is given as:
[tex]G(\dfrac{x_1+x_2+x_3}{3}, \dfrac{y_1+y_2+y_3}{3})[/tex]
Where [tex](x_1,y_1), (x_2,y_2)\ and\ (x_3,y_3)[/tex] are the coordinates of the vertices of the triangle.
As per the given values, we have:
[tex]x_1 = -4\\y_1 = -1\\x_2 = 2\\y_2 = 2\\x_3 = 2\\y_3 = -3[/tex]
Putting the values,we can find the coordinates of centroid as:
[tex]G(\dfrac{-4+2+2}{3}, \dfrac{-1+2-3}{3})\\\Rightarrow G(0, -\dfrac{2}{3})[/tex]
Therefore, the coordinates of the centroid is:
[tex]G(0, -\dfrac{2}{3})[/tex]
