Question

1. line k bisects line segment ac at point b. if ab = 6x - 2 and bc = 2(x + 9), then find ab.

Explanation:

Step1: Set AB equal to BC

Since line k bisects AC at B, AB = BC. So, $6x - 2=2(x + 9)$.

Step2: Expand the right - hand side

Using the distributive property, $2(x + 9)=2x+18$. The equation becomes $6x - 2=2x + 18$.

Step3: Subtract 2x from both sides

$6x-2x - 2=2x-2x + 18$, which simplifies to $4x-2 = 18$.

Step4: Add 2 to both sides

$4x-2 + 2=18 + 2$, resulting in $4x=20$.

Step5: Solve for x

Dividing both sides by 4, we get $x = 5$.

Step6: Find the length of AB

Substitute $x = 5$ into the expression for AB: $AB=6x-2=6\times5-2=30 - 2=28$.

Answer:

28