Exercise 53 Page 433

The centroid is the point of concurrency of the medians of a triangle. In the given diagram, P is the centroid.

Using the Concurrency of Medians Theorem, we can write an equation that we can use to find the desired length XK. XP = 2/3XK With the Segment Addition Postulate, we can rewrite XK as the sum of the two smaller segments. We are given that KP= 3, which we can substitute into this new equation. XK = XP+ KP ⇒ XK = XP+ 3 Next, we can form a system of equations that we can solve using the Substitution Method.

Finally, we can substitute XP=6 into the second equation to find XK.