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use betweenness of points to answer this question.

Is point W between points T and B?

Given: points W, T, and B are collinear. Also, mTW= 3/4, mWB= 1/3, and mTB= 13/12

1 answer

To determine if point W is between points T and B, we can use the property of points being collinear and the concept of betweenness.

The definition of betweenness states that if point W lies on line segment TB, then:

mTW + mWB = mTB

Given the distances:

  1. \( mTW = \frac{3}{4} \)
  2. \( mWB = \frac{1}{3} \)
  3. \( mTB = \frac{13}{12} \)

Let's add \( mTW \) and \( mWB \):

\[ mTW + mWB = \frac{3}{4} + \frac{1}{3} \]

To add these fractions, we need a common denominator. The least common multiple of 4 and 3 is 12.

Rewriting the fractions:

\[ \frac{3}{4} = \frac{9}{12}, \] \[ \frac{1}{3} = \frac{4}{12}. \]

Now, add them together:

\[ mTW + mWB = \frac{9}{12} + \frac{4}{12} = \frac{13}{12}. \]

Now we compare this result to \( mTB \):

\[ mTB = \frac{13}{12}. \]

Since \( mTW + mWB = mTB \), we can conclude that point W is indeed between points T and B.

Therefore, point W is between points T and B.