## anonymous one year ago What coordinate for F would make triangle ABC and triangle DEF congruent?

1. anonymous

2. anonymous

A) (-2,4) B) (-2,3) C) (-3,3) D) (-3,4)

3. anonymous

i believe that the answer is B , but that is just because i looked at the graph. its like an overlapping reflection, correct? i need help, i need someone to walk me through this . is there like, a formula? the lesson shows me this formula but its not clear on how to use it. $\sqrt{(y1-y2)^2+ (x1-x2)^2}$

4. anonymous

anone wanna assist me please? i wanna learn how to do this myself :(

5. anonymous

@ParthKohli @pooja195 @Data_LG2

6. anonymous

@hartnn @nincompoop @Abhisar

7. anonymous

@misty1212

8. baru

that formula you have typed out, do you know what it's for?

9. anonymous

@baru i THINK its to find the distance between two points, the lesson doesnt get detailed in it though :( they just start using it through examples

10. baru

you are right, its for the distance between two points. for two triangles to be congruent, the sides of the triangles should have equal lengths

11. baru

if you say triangle ABC congruent to DEF it means AB=DE BC=EF AC=DF

12. baru

with me so far?

13. anonymous

yes :)

14. anonymous

so how would i calculate f using the formula? would i use the distance between BC or Ac to find F or?...

15. baru

yeah..that would be the right way, but rather than solve for the co-ordinates of F, you are given several options for F, just substitute them and find EF and DF, see which one is equal to BC,AC

16. anonymous

so i use my options for F? and place them in the formula? im sorry if i dont quite understand, im a slow thinker in the morning :(

17. baru

yeah, exactly

18. baru

find the lengths EF and DF for each of the options, compare with the lengths AC and BC

19. anonymous

but how will i know it is right?

20. anonymous

@baru

21. anonymous

oh wait i THINK i understand, if they have the same result as the sides of the congruent triangle thats already there (abs) ?

22. anonymous

*c

23. baru

you have to do it for each option. only one option will give you EF=AC and DF=BC (you have to find lengths AC and BC as well)

24. anonymous

so i go all around? ok so first i find EF=AC right?

25. baru

first calculate AC and BC and write it down. then find EF for each option, see which one matches the value for AC that you just wrote down

26. anonymous

ok let me find AC and BC first

27. anonymous

@baru can you help me place the points into the formula? A = (1,-1) C= (2,3) B= (-1,2) C= (2,3)

28. baru

$AC = \sqrt{(1-2)^2 + (-1-3)^2}$

29. baru

$BC = \sqrt{(-1-2)^2 + (2-3)^2}$

30. anonymous

@baru but how did you place them? like which value was x1 x2 and y1 y2 ?

31. baru

oh...ok. wait. neglect what i typed just above, i have reversed the formula you gave(but it doesn't really matter). ill type it in detail, wait

32. baru

umm... how did you get A=(1,-1) ??

33. anonymous

i looked at the graph to see where the point is, did i saw it wrong? omg let me see haha

34. anonymous

is it (1,0)?

35. baru

yep :)

36. baru

so if you want to find the length AC then think of A =(x1,y1) and C=(x2,y2)

37. baru

so, x1=1 and y1=0 x2=2 and y2=3

38. anonymous

ohhhhhh kk hha now ill find AC

39. anonymous

i got 10 for AC

40. anonymous

AM I RIGHT? @baru

41. anonymous

lol i wanna make sure

42. anonymous

i have a feeling i am doing it wrong

43. anonymous

or is everything supoosed to stay in the sqr root ?

44. anonymous

so its supposed to be the sqr root of 10?

45. anonymous

46. baru

yep, AC is square root of 10.

47. anonymous

so then i find BC?

48. baru

not necessary, option 2 is the only one which gives you EF= square root of 10

49. baru

did you try finding EF for all the options?

50. anonymous

what do you mean?

51. baru

i'm sorry i meant DF

52. baru

we established that for the two triangles to be congruent, length AC = length DF

53. baru

you have found that the length AC is square root of ten. the question gives you several options for the co-ordinates of F. so find the length DF for each of the options, and see which one gives you square root of 10

54. anonymous

ohhhhhhhhhhhhhhhhhhhhhh ok ok ok so i can test B and see if it gives me squeare rot of 10? and if it does it means that my answer is correct? but if it isnt i keep testing the other options until it matches square root of 10?

55. baru

what do you mean "so i can test B' ?

56. anonymous

option b for F

57. baru

oh..lol. Yep, you are absolutely right then

58. anonymous

yay! lol

59. anonymous

kk ima test it

60. baru

alright

61. anonymous

@baru i got the square root of ten aswell!~ does this mean B is my answer? :)

62. baru

yup