Question

points a, b, c, and d on the figure below are collinear. use the figure for exercises 8 and 9.
a b c d
x 3x 4x − 13

1. if ac = 24, what is ab? 9. if bc = 15, what is bd?

Explanation:

Problem 8

Step1: Analyze AC composition

AC is AB + BC, so \( AC = AB + BC \). Given \( AB = x \), \( BC = 3x \), \( AC = 24 \). So \( x + 3x = 24 \).

Step2: Solve for x

Simplify \( 4x = 24 \), then \( x = \frac{24}{4} = 6 \).

Step1: Find x from BC

Given \( BC = 3x = 15 \), solve for x: \( x = \frac{15}{3} = 5 \).

Step2: Calculate BD

BD is BC + CD. CD is \( 4x - 13 \), substitute x = 5: \( CD = 4(5) - 13 = 20 - 13 = 7 \). Then \( BD = 15 + 7 = 22 \).

Answer:

\( AB = 6 \)

Problem 9