Question

points a, b, and c are collinear. point b is between a and c. let bc = 2x - 10, ab = 2x - 12, and ac = 10. find ab.
6
5
2
4

Explanation:

Step1: Use segment - addition postulate

Since points A, B, and C are collinear and B is between A and C, we have $AB + BC=AC$. Substitute the given expressions: $(2x - 12)+(2x - 10)=10$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $2x+2x-12 - 10 = 10$, which simplifies to $4x-22 = 10$.

Step3: Solve for x

Add 22 to both sides of the equation: $4x-22 + 22=10 + 22$, so $4x=32$. Then divide both sides by 4: $x = 8$.

Step4: Find the value of AB

Substitute $x = 8$ into the expression for AB. $AB=2x - 12$, so $AB=2\times8-12$. Calculate $2\times8-12=16 - 12=4$.

Answer:

4