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 a common point called the centroid.

Step2: Apply the property to the given problem

Since \(\overline{PS}\), \(\overline{QT}\), and \(\overline{RU}\) are medians of \(\triangle PQR\), they all intersect at the centroid. Given that \(\overline{PS}\) and \(\overline{QT}\) intersect at \((4,5)\), this point is the centroid. So, \(\overline{RU}\) (another median) must also intersect \(\overline{PS}\) at the centroid \((4,5)\).

Answer:

\((4,5)\)