Question

In δpqr, p^s―, q^t―, and r^u― are the medians, and p^s― and q^t― intersect at the point (4, 5). r^u― intersects p^s― at the point

a. (4, 5)
b. (5, 4)
c. (9, 2)
d. (2, 9)

Answer 1

The median r^u must intersect the other two medians p^s and q^t at the centroid of the triangle at point (4, 5), which is option a.

Step-by-step explanation:

In a triangle, the medians are the lines drawn from each vertex to the midpoint of the opposite side. The point where the medians intersect is called the centroid, which divides each median into parts that are in the ratio 2:1, with the longer part being closer to the vertex.

Given that medians p^s and q^t intersect at (4, 5), and the median r^u must also pass through this point to meet the other two medians at the centroid. So the median r^u must intersect p^s at (4, 5), which is option a. (4, 5).