Find L on A (-2,0) and B(4,3) that is 2/3 of the distance from A to B. A. (0,1)

B (1,3/2)

C(2/3, 3/2)

D(2,2)

Greetings from Brasil...

First we will calculate the distance between points A and B....

The expression that allows you to calculate the distance between two points is:

d(A; B) = √[(4 - (- 2))² + (3 - 0)²]

d(A; B) = √[6² + 3²]

45 = 3² · 5

d(A; B) = 3√5

L is 2/3 of the distance from AB, so

L = 2/3 · d(A; B)

L = 2/3 · 3√5

For the coordinates of point L: let us use similarity of triangles...

BM/LN = AB/AL     - refer to attached

3/Yl = 3√5/2√5

Yl = 2

As we can see in the graph, when Y = 2, X is also 2, so

there are other ways to accomplish this task

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068