Question

На координатной прямой отмечены точки A(3,5)иB(23)найди координату точки K, которая находится справа от точки B если известно что AK:KB=3:1 Ответ: K….. Ответьте пожалуйста быстреее

Answer 1

Ответ:

АК (29,25)

Пошаговое объяснение:

 А                                       В                    К

 ,                                         ,                      ,    

3,5                                    23                  29,25

Пусть КВ = х

Т.к. AK : KB = 3 : 1, то АК : КВ = 3х : х

АВ = В - А = 23 - 3,5 = 19,5

АК = АВ + КВ

3х = 19,5 + х  

3х - х = 19,5

2х = 19,5

х = 19,5/2

х = 9,75 - отрезок КВ

АК = 19,5 + 9,75 = 29,25

AK : KB = 3 : 1

29,25 : 9,75 = 3 : 1

Answer 2

Finding the Coordinate of Point K

To find the coordinate of point K, which is located to the right of point B, we need to use the given ratio of AK:KB, which is 3:1.

Let's start by finding the distance between points A and B on the number line. Point A is located at (3,5) and point B is located at (23). The distance between A and B can be calculated by subtracting the x-coordinates of the two points:

Distance AB = 23 - 3 = 20

Now, we need to divide this distance into four parts, with three parts representing AK and one part representing KB. Since the ratio of AK:KB is 3:1, we can calculate the length of AK and KB as follows:

AK = (3/4) * Distance AB = (3/4) * 20 = 15

KB = (1/4) * Distance AB = (1/4) * 20 = 5

To find the coordinate of point K, we need to add the length of AK to the x-coordinate of point A:

x-coordinate of K = x-coordinate of A + AK = 3 + 15 = 18

Therefore, the coordinate of point K is (18).

Please let me know if you have any further questions!