Question

In segment AC, the midpoint is B. If segments AC = 5x-9 and AB = 2x, what is the measure of segment AC.

Answer 1

Answer:

The measure of segment AC is 36 units

Step-by-step explanation:

- The mid-point divides the segment into two equal parts in length

- B is the mid point of segment AC

- That means B divides segment AC into two equal parts in length

∴ AB = BC

∵ AC = 5x - 9

∵ AB = 2x

- The two parts AB and BC are equal in length

∴ BC = 2x

∵ AC = AB + BC

- Substitute the values of AB and BC in the expression of AC

∴ AC = 2x + 2x

∴ AC = 4x

∵ AC = 5x - 9

- Equate the two values of AC

∴ 5x - 9 = 4x

- Add 9 to both sides

∴ 5x = 4x + 9

- Subtract 4x from both sides

∴ x = 9

- Substitute the value of x in any expression of AC

∵ AC = 4x

∵ x = 9

∴ AC = 4(9) = 36

* The measure of segment AC is 36 units