Applying the Segment Addition Postulate

What is the length of segment BC if segment BC measures 8x units in length and Point D is on segment BC?

Answer:

The length of segment BC is 8x units.

In this scenario, we are dealing with the Segment Addition Postulate, which states that for any three points A, B, and C on a line, if point B is between points A and C, then the length of segment AC is equal to the sum of the lengths of segments AB and BC.

Given that point D lies on segment BC, we have three points: A (point D), B (starting point of segment BC), and C (ending point of segment BC). According to the Segment Addition Postulate, the length of segment AC (or in this case, segment BC) is equal to the sum of the lengths of segments AB (or BD) and BC (or DC).

Mathematically, this can be expressed as:

BC = BD + DC

Given that segment BC measures 8x units in length, we can replace BC with 8x:

8x = BD + DC

Since point D is on segment BC, the lengths of segments BD and DC combined will give us the total length of segment BC. Therefore, the length of segment BC is indeed 8x units.

This conclusion is derived directly from the Segment Addition Postulate and the information provided in the question.