Point B is marked on segment AC. It is known that: AB: AC = 2: 7, and BC = 10 cm A) Find the length of the segments

Point B is marked on segment AC. It is known that: AB: AC = 2: 7, and BC = 10 cm A) Find the length of the segments: AB and AC B) Find the distance from point B to the midpoint of segment AC.

Since AB: AC = 2: 7, we denote AB as 2x, and AC as 7x. Then the distance from B to C is BC = 7x – 2x = 5x.

Since BC = 10 cm and BC = 5x, we calculate the value of x.

5x = 10.

x = 10: 5 = 2 cm.

1) Hence AB = 2x = 2 * 2 = 4 cm; AC = 7 * 2 = 14 cm.

2) Let O be the middle of AC. Then OA = OS = 14: 2 = 7 cm.

Point B lies between points A and O (since AB <BC).

AO = AB + BO.

BО = AO – AB = 7 – 4 = 3 cm.

Answer: 1) AB = 4 cm, AC = 14 cm.

2) The distance from B to the middle of the speaker is 3 cm.