In triangle PQR, PS, QT, and RU are the medians and PS and QT intersect at the point (4,5). RU intersects PS at the point.?

Solution:

In the given △PQR, PS, QT and RU are the medians of the given triangle.

It is given that PS and QT are intersecting at point (4, 5)

We know that the median of every triangle intersects each other at a common point known as the centroid of the triangle.

In the figure shown, O is the centroid of the triangle PQR

Also it is given in the question that PS and QT meet at the point (4, 5)

Also proved above the medians meet at the centroid

The point (4, 5) is the centroid of the triangle PQR

Now as RU is another median so it will also coincide the centroid

Therefore, RU intersects PS at the centroid i.e., at point (4, 5).

In triangle PQR, PS, QT, and RU are the medians and PS and QT intersect at the point (4, 5). RU intersects PS at the point.?

Summary:

In the △PQR, PS, QT, RU are the medians which coincide at the centroid of the triangle which is the point (4, 5).