Question

4. Точка Р належить відрізку EF, довжина якого дорів нює 24 см. Знайдіть відрізки EP i PF, якщо: 1) вiдрiзок ЕР на 6 см більший за відрізок PF; 2)EP: PF = 5 : 3. 5. Вiдрiзок АВ дорівнює 18 см. Точка N належить відрізку AB. Знайдіть відстань між серединами відрізків AN i NB. Будь ласка допоможіть дуже дуже терміново!!!!!!

Answer 1

Ответ:

4. 5х+3х=24

8х=24

х= 24/8

х=3

отже РF= 3*3=9, тоді ЕР=9+6=15

Answer 2

Problem 4: Finding the lengths of EP and PF

To find the lengths of EP and PF, we can use the given information that the length of EF is 24 cm and EP is 6 cm longer than PF.

Let's denote the length of PF as x. Since EP is 6 cm longer than PF, the length of EP can be expressed as (x + 6).

We know that the sum of the lengths of EP and PF is equal to the length of EF, which is 24 cm. Therefore, we can write the equation:

EP + PF = EF

Substituting the values we have:

(x + 6) + x = 24

Simplifying the equation:

2x + 6 = 24

Subtracting 6 from both sides:

2x = 18

Dividing both sides by 2:

x = 9

Now that we have the value of x, we can find the lengths of EP and PF:

EP = x + 6 = 9 + 6 = 15 cm

PF = x = 9 cm

Therefore, the lengths of EP and PF are 15 cm and 9 cm, respectively.

Problem 5: Finding the distance between the midpoints of AN and NB

To find the distance between the midpoints of AN and NB, we can use the given information that the length of AB is 18 cm.

Let's denote the midpoint of AN as M1 and the midpoint of NB as M2. We need to find the distance between M1 and M2.

The midpoint of a line segment is the point that divides the segment into two equal parts. Therefore, the length of AM1 is equal to the length of M1N, and the length of M2B is equal to the length of M2N.

Since AN is a line segment of length 18 cm, the length of AM1 and M1N is half of that, which is 9 cm.

Similarly, the length of M2B and M2N is also 9 cm.

To find the distance between M1 and M2, we can add the lengths of AM1 and M2B:

AM1 + M2B = 9 + 9 = 18 cm

Therefore, the distance between the midpoints of AN and NB is 18 cm.

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