Find the coordinates of the centroid of a triangle whose vertices are P(-6,1), Q(-2,-5) and R(8,1).
To find the centroid of a triangle, we take the average of the x-coordinates of the three vertices and the average of the y-coordinates of the three vertices.
The x-coordinate of the centroid is given by:
(x-coordinate of centroid) = (x-coordinate of P + x-coordinate of Q + x-coordinate of R)/3
= (-6 + (-2) + 8)/3
= 0/3
= 0
The y-coordinate of the centroid is given by:
(y-coordinate of centroid) = (y-coordinate of P + y-coordinate of Q + y-coordinate of R)/3
= (1 + (-5) + 1)/3
= -3/3
= -1
Therefore, the coordinates of the centroid of the triangle are (0, -1).
To find the coordinates of the centroid of a triangle, you can use the following formula:
Centroid (G) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
Let's apply this formula to the given triangle with vertices P(-6,1), Q(-2,-5), and R(8,1).
x-coordinate of the centroid (G):
(x1 + x2 + x3)/3 = (-6 - 2 + 8)/3 = 0/3 = 0
y-coordinate of the centroid (G):
(y1 + y2 + y3)/3 = (1 - 5 + 1)/3 = -3/3 = -1
Therefore, the centroid of the triangle with vertices P(-6,1), Q(-2,-5), and R(8,1) is G(0,-1).