## anonymous one year ago A point Q on a segment with endpoints A(2, −1) and C(4, 2) partitions the segment in a 3:1 ratio. Find Q. You must show all work to receive credit.

1. anonymous

@jim_thompson5910

2. jim_thompson5910

|dw:1434595427880:dw|

3. jim_thompson5910

|dw:1434595479540:dw|

4. jim_thompson5910

|dw:1434595574638:dw|

5. jim_thompson5910

Draw in segments to form a right triangle |dw:1434595636414:dw|

6. jim_thompson5910

what is this distance here? |dw:1434595691088:dw|

7. anonymous

the distance there i think is 2

8. jim_thompson5910

yes

9. jim_thompson5910

what is this distance here? |dw:1434595871048:dw|

10. jim_thompson5910

any ideas?

11. anonymous

the distance there is 4

12. jim_thompson5910

no

13. jim_thompson5910

|dw:1434596145144:dw|

14. jim_thompson5910

are you still stuck?

15. anonymous

@jim_thompson5910 sorry i was away from my computer but i am alittle sorry

16. jim_thompson5910

thats ok

17. anonymous

oh so would the distance be 2 then @jim_thompson5910

18. jim_thompson5910

3 actually |dw:1434597964616:dw|

19. jim_thompson5910

y = -1 to y = 2 is 3 units

20. anonymous

oh ok i understand now (:

21. jim_thompson5910

|dw:1434598022998:dw|

22. jim_thompson5910

"segment in a 3:1 ratio" means we have 3+1 = 4 parts total so cut vertical and horizontal segments into 4 equal parts |dw:1434598057496:dw|

23. anonymous

oh ok so now i divide 2 by 3 right (:

24. jim_thompson5910

the horizontal length 2 gets cut into 4 equal parts 2/4 = 1/2 = 0.5 so each little piece along the horizontal portion is 0.5 units long |dw:1434598108224:dw|

25. jim_thompson5910

agreed?

26. anonymous

agreed

27. jim_thompson5910

since we want 3:1 ratio, we go 3 parts in the horizontal direction to land here |dw:1434598197534:dw|

28. jim_thompson5910

that is 3*0.5 = 1.5 units to the right of point A

29. jim_thompson5910

x coordinate of A is x = 2 add on 1.5 2+1.5 = 3.5

30. jim_thompson5910

|dw:1434598259483:dw|

31. jim_thompson5910

we'll do the same for the vertical component the vertical component is 3 units high cut that into 4 parts 3/4 = 0.75 each vertical tiny piece is 0.75 units |dw:1434598214545:dw|

32. jim_thompson5910

and we go up 3 units 3*0.75 = 2.25 add 2.25 to the y coordinate of A -1+2.25 = 1.25 so y = 1.25 |dw:1434598278518:dw|

33. jim_thompson5910

put the two together to form point Q |dw:1434598294297:dw|

34. anonymous

oh ok i add the numbers up and got 4.75 correct (:

35. jim_thompson5910

no they just want the coordinates of Q

36. jim_thompson5910

you don't add the coordinates of Q

37. anonymous

oh ok so should i divide

38. jim_thompson5910

the final answer they want is Q Q is the point (3.5, 1.25)

39. jim_thompson5910

of course you have to show how you get point Q

40. anonymous

oh ok i see what mean