Use betweenness of points to answer this question.

Question

Is point Y between points T and Z? Given: Points Y, T, and Z are collinear. Also, mYZ=2.7, mTZ=1.9, and mTY=4.6

Answer 1

To determine if point Y is between points T and Z, we can use the properties of collinear points and the given distances.

We have the following distances:

• \( mYZ = 2.7 \)
• \( mTZ = 1.9 \)
• \( mTY = 4.6 \)

According to the definition of betweenness of points, if point Y is between points T and Z, then the sum of the distances from T to Y and Y to Z should equal the distance from T to Z.

We can check this as follows:

1. Calculate \( mTY + mYZ \): \[ mTY + mYZ = 4.6 + 2.7 = 7.3 \]

2. Compare this sum with \( mTZ \):

   • Given \( mTZ = 1.9 \)

Since \( mTY + mYZ = 7.3 \) does not equal \( mTZ = 1.9 \), this means that point Y is not between points T and Z.

Thus, point Y is not between points T and Z.