Practice Problem #1
By: Oliver Shi
Given triangle with points: A(0, 6) B(0, 3) and (0, -3), and centroid O, find the length of OA.
My first step would be to graph △ABC on a coordinate plane.
My next step would be to get all the medians and label the centroid O.
To get the median of ∠A , you'd get the midpoint of the opposite side, CB ((-3 + 3)/2, (0 + 0)/2) -> (0, 0) and draw a line connecting A to this midpoint. To get the median of ∠B, you'd get the midpoint of the the opposite side, AC ((-3 + 0)/2, (0 + 6)/2) -> (-1.5, 3) and draw a line connecting B to this midpoint. To get the median of ∠C, you'd get the midpoint of the the opposite side, AB ((3 + 0)/2, (0 + 6)/2) -> (1.5, 3) and draw a line connecting C to this midpoint. Now, label the point of concurrency "O". Since I've found centroid O(0, 2) I can now find the length of AO.
By applying the distance formula sqroot[(0 - 0)^2 + (6 - 2)^2] -> sqroot[(0)^2 + (4)^2] -> sqroot(0 + 16) -> sqroot(16) -> 4 which would be the length of AO |