Question

select the correct answer from the drop - down menu.
in \\( \triangle p q r, \overline{p s}, \overline{q t} \\), and \\( \overline{r u} \\) are the medians, and \\( \overline{p s} \\) and \\( \overline{q t} \\) intersect at the point \\( (4,5) \\).
\\( \overline{r u} \\) intersects \\( \overline{p s} \\) at the point

Explanation:

Step1: Recall the property of the centroid of a triangle

The medians of a triangle intersect at the centroid.

Step2: Use the property of centroid intersection

Since all three medians of a triangle intersect at the same point (the centroid), if \(\overline{PS}\) and \(\overline{QT}\) intersect at \((4,5)\), then \(\overline{RU}\) (the third median) must also intersect \(\overline{PS}\) at the centroid \((4,5)\).

Answer:

\((4,5)\)