Find the centroids of the triangles whose vertices are given below.(4, 7), (8, 4), (7, 11)
Find the centroids of the triangles whose vertices are given below.(4, 7), (8, 4), (7, 11)
(4, 7), (8, 4), (7, 11)
The centroid of the triangle formed by the given coordinates is
\[= \left( \frac{4 + 8 + 7}{3}, \frac{7 + 4 + 11}{3} \right)\]
\[ = \left( \frac{19}{3}, \frac{22}{3} \right)\]
\[= \left( \frac{4 + 8 + 7}{3}, \frac{7 + 4 + 11}{3} \right)\]
\[ = \left( \frac{19}{3}, \frac{22}{3} \right)\]
Explanation:-
To find the centroid of a triangle, we need to take the average of the coordinates of its three vertices.
The coordinates of the given vertices are:
A = (4, 7) B = (8, 4) C = (7, 11)
To find the x-coordinate of the centroid, we take the average of the x-coordinates of A, B, and C:
x-coordinate of centroid = (4 + 8 + 7) / 3 = 19 / 3
To find the y-coordinate of the centroid, we take the average of the y-coordinates of A, B, and C:
y-coordinate of centroid = (7 + 4 + 11) / 3 = 22 / 3
Therefore, the coordinates of the centroid of the triangle formed by the given coordinates are (19/3, 22/3).
Chapter 5. Co-ordinate Geometry – Practice Set 5.2 (Page 115)