Question

points a, b, and c are collinear. point b is between a and c. find the length indicated.

1. find ac if ac = 2x + 6, ab = 10, and bc = x + 4.

1.) draw your line
2.) plot your points
3.) find x
4.) find ac

Explanation:

Step1: Use segment - addition postulate

Since points A, B, and C are collinear and B is between A and C, we have $AC = AB+BC$. Given $AC = 2x + 6$, $AB = 10$, and $BC=x + 4$, we set up the equation $2x+6=10+(x + 4)$.

Step2: Simplify the right - hand side of the equation

$2x+6=10+x + 4$ simplifies to $2x+6=x + 14$.

Step3: Solve for x

Subtract x from both sides: $2x - x+6=x - x + 14$, which gives $x+6=14$. Then subtract 6 from both sides: $x=14 - 6$, so $x = 8$.

Step4: Find the length of AC

Substitute $x = 8$ into the expression for AC. $AC=2x+6=2\times8+6=16 + 6=22$.

Answer:

1. (Drawing a line is a visual task and hard to represent in text. But conceptually, draw a straight - line.)
2. (Plot points A, B, and C on the line with B between A and C)
3. $x = 8$
4. $AC = 22$