Question

using the segment addition postulate, which is true?
number line with points a (at -6), b (at -1), c (at 2), d (at 8)
options:

• ( ab + bc = ad )
• ( ab + bc = cd )
• ( bc + cd = ad )
• ( bc + cd = bd )

Explanation:

Step1: Identify coordinates of points

First, find the coordinates of points A, B, C, D from the number line:

• A is at -6, B at -1, C at 2, D at 8.

Step2: Calculate lengths of segments

Calculate the length of each segment using the distance formula (since it's a number line, length is difference of coordinates):

• \( AB = | -1 - (-6) | = |5| = 5 \)
• \( BC = | 2 - (-1) | = |3| = 3 \)
• \( CD = | 8 - 2 | = |6| = 6 \)
• \( AD = | 8 - (-6) | = |14| = 14 \)
• \( BD = | 8 - (-1) | = |9| = 9 \)

Step3: Check each option

• Option 1: \( AB + BC = 5 + 3 = 8 \), \( AD = 14 \). \( 8

eq 14 \), so false.

• Option 2: \( AB + BC = 8 \), \( CD = 6 \). \( 8

eq 6 \), so false.

• Option 3: \( BC + CD = 3 + 6 = 9 \), \( AD = 14 \). \( 9

eq 14 \), so false.

• Option 4: \( BC + CD = 3 + 6 = 9 \), \( BD = 9 \). \( 9 = 9 \), so true.

Answer:

D. \( BC + CD = BD \)