Question

На прямой расположены пять точек A, B, C, В и E так, что AC = 5 см, AE = 4 см, BC = 14 см, BD = 2 см, DE = 3 см. Найдите расстояние между серединами отрезков BE и AC. Сделайте рисунок.

Answer 1

МК=9см
На рисунке всё наглядно показано

Answer 2

Problem Analysis

We are given five points, A, B, C, D, and E, with specific distances between them. We need to find the distance between the midpoints of segments BE and AC.

Solution

To find the distance between the midpoints of segments BE and AC, we need to find the coordinates of the midpoints first. Let's label the coordinates of the points as follows:

A(xA, yA), B(xB, yB), C(xC, yC), D(xD, yD), E(xE, yE)

Using the given distances, we can calculate the coordinates of the midpoints as follows:

Midpoint of BE: M(xM, yM) xM = (xB + xE) / 2 yM = (yB + yE) / 2

Midpoint of AC: N(xN, yN) xN = (xA + xC) / 2 yN = (yA + yC) / 2

Now that we have the coordinates of the midpoints, we can calculate the distance between them using the distance formula:

Distance between M and N: MN = sqrt((xM - xN)^2 + (yM - yN)^2)

Let's substitute the given values into the formulas and calculate the distance.

Calculation

Given: AC = 5 cm AE = 4 cm BC = 14 cm BD = 2 cm DE = 3 cm

Using the given distances, we can calculate the coordinates of the midpoints as follows:

Midpoint of BE: M(xM, yM) xM = (xB + xE) / 2 yM = (yB + yE) / 2

Midpoint of AC: N(xN, yN) xN = (xA + xC) / 2 yN = (yA + yC) / 2

Now let's substitute the given values into the formulas and calculate the distance between the midpoints.

Calculation

Given: AC = 5 cm AE = 4 cm BC = 14 cm BD = 2 cm DE = 3 cm

Using the given distances, we can calculate the coordinates of the midpoints as follows:

Midpoint of BE: M(xM, yM) xM = (xB + xE) / 2 yM = (yB + yE) / 2

Midpoint of AC: N(xN, yN) xN = (xA + xC) / 2 yN = (yA + yC) / 2

Now let's substitute the given values into the formulas and calculate the distance between the midpoints.

Using the given distances, we can calculate the coordinates of the midpoints as follows:

Midpoint of BE: M(xM, yM) xM = (xB + xE) / 2 = (0 + 14) / 2 = 7 yM = (yB + yE) / 2 = (0 + 3) / 2 = 1.5

Midpoint of AC: N(xN, yN) xN = (xA + xC) / 2 = (0 + 5) / 2 = 2.5 yN = (yA + yC) / 2 = (0 + 0) / 2 = 0

Now we can calculate the distance between the midpoints using the distance formula:

MN = sqrt((xM - xN)^2 + (yM - yN)^2) = sqrt((7 - 2.5)^2 + (1.5 - 0)^2) = sqrt(4.5^2 + 1.5^2) = sqrt(20.25 + 2.25) = sqrt(22.5) ≈ 4.74 cm

Therefore, the distance between the midpoints of segments BE and AC is approximately 4.74 cm.

Diagram

Here is a diagram representing the given points and the midpoints of segments BE and AC:

A----------------C
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|                |
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B----------------E
       M     N

Please note that the diagram is not to scale and is only for illustrative purposes.

I hope this helps! Let me know if you have any further questions.