Final answer:
The correct answer is option D, where the centroid of the triangle is located at coordinates (-5,-2), calculated by taking averages of the triangle's vertex coordinates.
Step-by-step explanation:
The correct answer is option D. The coordinates of the centroid of a triangle can be found by taking the average of the x-coordinates and the y-coordinates of the triangle's vertices. In this case, we will apply the formula for finding the centroid (G), which is given by G=(x1+x2+x3)/3, (y1+y2+y3)/3. Using the vertices D (0,0), E (-8,0), and F (-7, -6):
The coordinates of the centroid of a triangle can be found by taking the average of the x-coordinates and the average of the y-coordinates of the three vertices. Let's calculate:
D (0,0)
E (-8,0)
F (-7,-6)
Adding the x-coordinates and dividing by 3, we get (0 + (-8) + (-7))/3 = -5
Adding the y-coordinates and dividing by 3, we get (0 + 0 + (-6))/3 = -2
So, the coordinates of the centroid are (-5, -2).
- The average of the x-coordinates: (0 - 8 - 7) / 3 = -15 / 3 = -5
- The average of the y-coordinates: (0 + 0 - 6) / 3 = -6 / 3 = -2
Thus, the centroid G is at (-5, -2).