Question

If T is the centroid of ΔMNP, QP = 45, MT = 48, NQ = 54, RT = 10, what is the ratio of the distance from T to P to the distance from T to Q?

(A) 3:2
(B) 2:3
(C) 4:3
(D) 3:4

Answer 1

The ratio of the distance from T to P to the distance from T to Q is 24:5.

Step-by-step explanation:

To find the ratio of the distance from T to P to the distance from T to Q, we can use the properties of centroids in triangles. Since T is the centroid of triangle MNP, the ratio of the distances is equal to the ratio of the corresponding sides. The distance from T to P is represented by PT, and the distance from T to Q is represented by QT. Thus, the ratio of PT to QT is equal to the ratio of the sides MP to NQ. Using the given information, we have:

1. MP = 2 * MT = 2 * 48 = 96
2. NQ = 2 * RT = 2 * 10 = 20

So, the ratio of PT to QT is 96:20, which simplifies to 24:5. Therefore, the answer is (D) 24:5.