Question

На отрезке AB=40см выбрана точка P. Найдите расстояние между середина и отрезков АР и РВ.

Answer 1

Дано: AC = CP, PD = DB, AB = 40 см

Найти: CD

Решение:

AP + PB = AB = 40 см

CD = AP : 2 + PB : 2 = AB : 2 = 40 : 2 = 20 см

Ответ: Расстояние между серединами отрезков AP и PB = 20 см.

Answer 2

Problem Analysis

We are given a line segment AB with a length of 40 cm. We need to find the distance between the midpoint of segment AP and the midpoint of segment PV.

Solution

To find the distance between the midpoints of segments AP and PV, we need to find the lengths of segments AP and PV first.

Let's assume that point P divides segment AB into two parts, AP and PV, such that AP is x cm long and PV is (40 - x) cm long.

Since P is the midpoint of segment AP, the length of segment AP is twice the length of segment PP'. Similarly, the length of segment PV is twice the length of segment P'V, where P' is the midpoint of segment AB.

Therefore, the length of segment AP is 2x cm, and the length of segment PV is 2(40 - x) cm.

Now, we can find the midpoint of segment AP by dividing the length of segment AP by 2. Similarly, we can find the midpoint of segment PV by dividing the length of segment PV by 2.

Finally, we can find the distance between the midpoints of segments AP and PV by subtracting the coordinates of the two midpoints.

Let's calculate the solution step by step:

1. Length of segment AP = 2x cm 2. Length of segment PV = 2(40 - x) cm 3. Midpoint of segment AP = (x/2, 0) 4. Midpoint of segment PV = (40 - x/2, 0) 5. Distance between the midpoints = (40 - x/2) - (x/2) = 40 - x cm

Therefore, the distance between the midpoints of segments AP and PV is 40 - x cm.

Answer

The distance between the midpoint of segments AP and PV is 40 - x cm.

Note: The value of x is not provided in the question, so we cannot calculate the exact distance without that information.