Question

ПОЖАЛУЙСТА СРОЧНОЧерез конец A отрезка AN проведена плоскость α, а через точку B отрезка AN проведён отрезок BM длиной 9 см, параллельный плоскости α. Прямая NM пересекает плоскость α в точке C. Найдите расстояние между точками плоскости A и C, если известно, что NB : BA = 3 :7.

Answer 1

Ответ:

BM параллельна плоскости альфа, значит BM параллельна QА, значит треугольники MBK и QAK подобны с коэффициентом подобия 4/11 (AK/BK = 11x/4x).

А это значит, что MB/QA = 4/11. Подставляем значение отрезка MB и находим QA

QA = 22

Ответ: 22см....

Объяснение:

поставь лудший ответ пж ‍♂️

Answer 2

Problem Analysis

We are given a line segment AN, and a plane α passing through the end A of the segment. Another line segment BM is drawn through the point B on the segment AN, parallel to the plane α. The line NM intersects the plane α at point C. We need to find the distance between the points A and C, given that NB:BA = 3:7 and the length of BM is 9 cm.

Solution

To find the distance between points A and C, we need to determine the length of the line segment AC. Let's break down the problem step by step:

1. Find the length of segment AB: - We are given that NB:BA = 3:7. - Let's assume the length of NB is x. Then the length of BA is 7x. - We are also given that the length of BM is 9 cm. - Therefore, the length of AM is AB - BM = 7x - 9.

2. Find the length of segment NC: - Since segment BM is parallel to plane α, segment NC is parallel to segment AB. - Therefore, the ratio of lengths of segments NC and AB is the same as the ratio of lengths of segments NB and BA. - NB:BA = 3:7, so NC:AB = 3:7. - Let's assume the length of NC is y. Then the length of AB is 7y. - Therefore, the length of NC is 3y.

3. Find the length of segment AC: - The length of AC is the sum of the lengths of segments AM and NC. - AC = AM + NC = 7x - 9 + 3y.

Now, we need to find the values of x and y to calculate the length of AC.

Calculation

To find the values of x and y, we can use the given information that NB:BA = 3:7.

Let's assume the length of NB is 3k and the length of BA is 7k, where k is a constant.

From the given information, we know that the length of BM is 9 cm. Therefore, the length of AM is 7k - 9.

Since segment BM is parallel to plane α, segment NC is parallel to segment AB. Therefore, the ratio of lengths of segments NC and AB is the same as the ratio of lengths of segments NB and BA.

Using the ratio of NB:BA = 3:7, we can write the equation:

NB/BA = 3/7

Substituting the lengths of NB and BA:

(3k)/(7k) = 3/7

Simplifying the equation:

3k/7k = 3/7

Cross-multiplying:

7 * 3k = 3 * 7k

21k = 21k

This equation is true for any value of k. Therefore, we can choose any value for k.

Let's assume k = 1.

Then, the length of NB is 3 cm and the length of BA is 7 cm.

Substituting these values into the equation for the length of AC:

AC = AM + NC = (7 * 1 - 9) + (3 * 1) = -2 + 3 = 1 cm

Therefore, the distance between points A and C is 1 cm.

Answer

The distance between the points A and C, given that NB:BA = 3:7 and the length of BM is 9 cm, is 1 cm.