## anonymous one year ago The table shows the proof of the relationship between the slopes of two perpendicular lines. What is the missing statement in step 2?

1. anonymous

1. is similar to . given 2. property of similar triangles 3. = property of proportion 4. slope of = slope of = definition of slope 5. slope of × slope of = multiplying the slopes 6. (This statement is intentionally left blank.) Substitution Property of Equality 7. slope of × slope of = -1 simplifying the right side

2. anonymous

couldnt get all of it but tried my best

3. jim_thompson5910

a screenshot is best because we can see the full problem (even the missing symbols)

4. anonymous

1. AC←→⊥CD←→ (view diagram) ΔABC is similar to ΔCED. given 2. (This statement is intentionally left blank.) property of similar triangles 3. ABBC = ECDE property of proportion 4. slope of AC←→ = -ABBC slope of DC←→ = DEAC definition of slope 5. slope of AC←→ × slope of DC←→ = -ABBC×DEEC multiplying the slopes 6. Substitution Property of Equality 7. slope of AC←→ × slope of DC←→ = -1 simplifying the right side

5. anonymous

sorry here it is

6. jim_thompson5910

well step 3 has AB*BC = EC*DE, or so it seems the step before that would be some proportion and cross multiplying would lead to step 3

7. jim_thompson5910

does that make sense?

8. anonymous

not really but u can explain it in detail. mabye ill get it

9. jim_thompson5910

let's say you had a/b = c/d

10. jim_thompson5910

if you cross multiplied, you'd get a*d = b*c agreed?

11. anonymous

yea

12. jim_thompson5910

so what proportion could be set up to lead to AB*BC = EC*DE ?

13. anonymous

they seem to look like this but in fraction AB/BC;. something like that.

14. anonymous

AB/DE, and EC/DE

15. jim_thompson5910

more like AB/EC = DE/BC. There are other possibilities |dw:1436929680423:dw|

16. jim_thompson5910

|dw:1436929728958:dw|

17. anonymous

oops sorry. thats not on my answer choices tho

18. anonymous

the closest choice has a fraction DE/EC. would that work?

19. jim_thompson5910

well as long as they cross multiply to AB*BC = EC*DE, then it will work

20. jim_thompson5910

there are more possibilities than what I drew up there (maybe 4 possibilities?)

21. anonymous

ok hold on

22. anonymous

AB/EC=BC/DE AB/BC=DE/EC AB=DE BC=EC AB/BC= -EC/DE

23. anonymous

24. jim_thompson5910

choice C looks funky...there are no fractions there?

25. jim_thompson5910

try posting a screenshot if you can

26. anonymous

there are no fractions in c, and sorry i cant post a screenshot.

27. jim_thompson5910

ok let me think

28. jim_thompson5910

in line 3, where it says `3. ABBC = ECDE property of proportion` there are no fractions here either?

29. anonymous

actually yea those are fractions

30. anonymous

its really hard to paste those kinds of things on here.

31. jim_thompson5910

so line 3 actually says this right? AB/BC = EC/DE

32. anonymous

yes yes

33. jim_thompson5910

|dw:1436930874242:dw|

34. jim_thompson5910

you can multiply both sides by BC and divide both sides by EC that will make BC and EC swap |dw:1436930925056:dw|

35. jim_thompson5910

giving |dw:1436930949685:dw|

36. anonymous

omg thanks so much!

37. anonymous

can you help me with one more? its a mastery, and i didnt really understand this lesson

38. jim_thompson5910

sure

39. anonymous

AB and BC form a right angle at point B. If A = (-3, -1) and B = (4, 4), what is the equation of BC

40. jim_thompson5910

first find the equation of the line through A and B

41. anonymous

slope?

42. anonymous

5/7 is the slope

43. jim_thompson5910

use that slope to find the equation of the line through those two points

44. jim_thompson5910

you can use y = mx+b

45. anonymous

i think its y=5/7x+8/7

46. jim_thompson5910

yep

47. jim_thompson5910

|dw:1436931657035:dw|

48. jim_thompson5910

AB and BC form a right angle, so |dw:1436931712083:dw|

49. jim_thompson5910

what is the slope of BC ?

50. anonymous

x + 3y = 16 2x + y = 12 -7x − 5y = -48 7x − 5y = 48

51. anonymous

these are the answer choices btw. and the slope for BC is -7/5 right?

52. jim_thompson5910

what is the equation of the line going through B and has slope of -7/5

53. jim_thompson5910

use y = mx+b