Find the centroid of the triangle whose vertices are the points A(−1,−3),B(0,4), and C(5,1). Measure the distance from M to each vertex and M to each opposite side. What ratio do you notice?

Question

Please help in this subject, Partitioning Directed Segments on the Coordinate Plane

Answer 1

(1) centroid of triangle:

-add all x values from 3 vertices and divide by 3

-add all y values from 3 vertices and divide by 3

x-coordinate for centroid: (-1+0+5)/(3) = -4/3

y-coordinate for centroid: (-3+4+1)/(3) = 2/3

centroid is at (-4/3,2/3)

(2) I'm guessing M, in this case, means midpoint perhaps. The midpoint will always be equidistant from each vertex and each opposite side. So, the ratio should be the same for all calculations.

Let me know if that helps, and feel free to reach out if you have more questions!