Question

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

a) (4,5)
b) (5,4)
c) (4,4)
d) (3,5)

Answer 1

In triangle PQR, the medians PS, QT, and RU intersect at the centroid, which is given as point (4,5). Since medians intersect at the centroid, RU also intersects PS at point (4,5), which is option (a).

Step-by-step explanation:

The subject of this question is Mathematics, specifically geometry involving medians of a triangle. Medians are line segments from a triangle's vertex to the midpoint of the opposite side, and in any triangle, they intersect at a single point known as the centroid. The question describes triangle PQR with medians PS, QT, and RU, stating that PS and QT intersect at point (4,5). This intersection point is the centroid of the triangle. Since all medians of a triangle intersect at the centroid, median RU must also pass through the point (4,5). Consequently, the answer to where RU intersects PS is option (a) (4,5).