Triangle ABC is drawn on a coordinate plane with vertices A(−3,−3) , B(0,6) , and C(4,−3) and medians indicating the midpoint of each of the lines AB , BC , and CA . Prove the medians meet at a single point by finding the centroid.(1 point) Responses (13,1) left parenthesis Start Fraction 1 over 3 End Fraction comma 1 right parenthesis (0,13) left parenthesis 0 comma Start Fraction 1 over 3 End Fraction right parenthesis (16,3) left parenthesis Start Fraction 1 over 6 End Fraction comma 3 right parenthesis (13,0)
To find the centroid of triangle ABC, we can use the formulas:
x-coordinate of centroid = (x1 + x2 + x3) / 3
y-coordinate of centroid = (y1 + y2 + y3) / 3
Using the coordinates of points A, B, and C, we have:
x1 = -3, y1 = -3
x2 = 0, y2 = 6
x3 = 4, y3 = -3
x-coordinate of centroid = (-3 + 0 + 4) / 3 = 1/3
y-coordinate of centroid = (-3 + 6 - 3) / 3 = 0
Therefore, the centroid of triangle ABC is (1/3, 0).