Question

use \\( \triangle a b c \\), shown to the right, to answer the following question. if \\( b k = 13 \\), what is \\( k q \\)? \\( k q = \square \\)

Explanation:

Step1: Recall the centroid property

The centroid of a triangle divides each median in a ratio of \(2:1\). In \(\triangle ABC\), \(K\) is the centroid (intersection of medians \(AP\) and \(BQ\)). Let \(KQ = x\) and \(BK=2x\).

Step2: Solve for \(x\)

Given \(BK = 13\), and since \(BK = 2KQ\) (from centroid - median ratio property). Then \(x=\frac{BK}{2}\). Substitute \(BK = 13\) into the formula: \(KQ=\frac{13}{2}=6.5\)

Answer:

\(6.5\)