Question

Отрезок AB пересекает плоскость а в точке О. Конец B отрезка отстоит от плоскости а на расстоянии 8. На каком расстоянии от плоскости а находится конец A отрезка , если известно, что точкой О отрезок AB делится в отношении АО:OB=3:2

Answer 1

Решение:

8 / 2 = 4 (приходится на одну часть)

АО = 4 * 3 = 12см 

Answer 2

Given information:

- The line segment AB intersects the plane at point O. - The endpoint B of the line segment is 8 units away from the plane. - The line segment AB is divided in the ratio AO:OB = 3:2.

To find:

The distance from the plane to the endpoint A of the line segment AB.

Solution:

Let the distance from the plane to the endpoint A be x.

Since the line segment AB is divided in the ratio AO:OB = 3:2, we can express the length of AO as 3k and the length of OB as 2k, where k is a scaling factor.

From the given information, we know that the distance from the endpoint B to the plane is 8 units. Therefore, we can write the following equation:

2k + 8 = x

To find the value of k, we can use the fact that the line segment AB intersects the plane at point O. This means that the sum of the lengths of AO and OB should be equal to the length of AB. Since the length of AO is 3k and the length of OB is 2k, we have:

3k + 2k = AB

Simplifying the equation, we get:

5k = AB

Now, we can substitute the value of AB in terms of k into the equation for the distance x:

2k + 8 = x

Substituting AB = 5k into the equation, we have:

2k + 8 = x

Now, we can solve for x:

x = 2k + 8

Since AB = 5k, we can substitute AB = 5k into the equation for x:

x = 2(AB/5) + 8

Simplifying the equation, we get:

x = (2/5)AB + 8

Therefore, the distance from the plane to the endpoint A of the line segment AB is (2/5) times the length of AB plus 8 units.