Question

points a, b, and c are collinear. if bc = 8.5 and ac = 13.2, select all possible values of ab. a. 4.7 b. 3.8 c. 21.7 d. 8.5 e. 13.2

Explanation:

Step1: Analyze the two cases of collinear points

When three points \( A \), \( B \), \( C \) are collinear, there are two possible arrangements:

• Case 1: \( B \) lies between \( A \) and \( C \). Then \( AC = AB + BC \), so \( AB=AC - BC \).
• Case 2: \( C \) lies between \( A \) and \( B \). Then \( AB = AC+BC \).

Step2: Calculate for Case 1

Given \( BC = 8.5 \) and \( AC = 13.2 \), for Case 1:
\( AB=AC - BC=13.2 - 8.5 = 4.7 \)

Step3: Calculate for Case 2

For Case 2:
\( AB = AC + BC=13.2+8.5 = 21.7 \)

Answer:

A. 4.7, C. 21.7