## anonymous one year ago Triangle ABC has been rotated 90° to create triangle DEF. Using the image below, prove that perpendicular lines have opposite and reciprocal slopes. You must show all of your work to receive credit.

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1. anonymous

2. anonymous

please help, i have 3 weeks untill i go to boot camp and i have to finish school.

3. phi

can you "read off" the (x,y) coords for points B and C ?

4. anonymous

B (5, 4) C (1, 1)

5. phi

ok on C for B, you want the "sideways" number (the x) first you did it backwards.

6. anonymous

my bad, i havent always been real sharp in math, physics and space science are my thing

7. phi

I assume you figured out we have B( 4,5), C(1,1) now find the slope. slope is change in y divided by change in x can you do that ?

8. anonymous

yes

9. anonymous

is the slope 1?

10. phi

change in "y" means subtract the y values , for example y value of pt B - y value of pt C what do you get ?

11. anonymous

so i would subtract 5 from 4? or the other way around

12. phi

neither. the y value of point B (4,5) is the 2nd number in that pair then you find the y value of point C (1,1)

13. anonymous

I'm lost

14. phi

ok, try this put your finger on point C in the graph count straight up until you are at the same height as point B how many steps up is that ?

15. anonymous

4

16. phi

now count to the right until you get to point B if you move right, count that as a positive number how many steps do you move sideways?

17. anonymous

3

18. phi

you just found change in y (up 4) and change in x (3 to the right) or rise/run (is how some people call it) in other words, the slope is 4/3 (that is change in y divided by change in x) now we have to find the slope of the other line.

19. phi

can you find the change in y from point F to pt E ?

20. anonymous

4/4

21. phi

no. just put your finger on pt F, and count up until you are at the same height as point E how many steps up ?

22. anonymous

sorry 3/4

23. phi

almost. if you start at F and go up 3 steps that is +3 for change in y but when you move sideways you go left 4 steps. write that as -4 (if you went in the other direction, to the right, that would be plus) what is the slope?

24. anonymous

3/-4

25. phi

yes, or just $- \frac{3}{4}$ (it means the same thing) lines are perpendicular if when you multiply their slopes, you get -1 what do you get when you multiply $\frac{4}{3} \cdot - \frac{3}{4}$?

26. anonymous

i got 1/1 which is just 1

27. anonymous

28. phi

I would write it this way: multiply top times top and bottom times bottom $\frac{4}{3} \cdot - \frac{3}{4}= - \frac{12}{12} = -1$

29. phi

they want you to show your work, so they may want to see how to calculate the slope (rather than count steps on the graph)

30. anonymous

ok

31. phi

F (-1,1) E(-5,4) change in y is 1 - 4 = -3 change in x is -1 - -5= -1+5 = 4 change in y divided by change in x is -3/4 = - 3/4

32. anonymous

okay its kinda starting to make sense

33. anonymous

is that the final product

34. anonymous

you can have your medal back when you come back...

35. phi

they want you to **prove that perpendicular lines have opposite and reciprocal slopes*** (though I would say "negative reciprocal") to do that , and show your work find the slope of each line. I showed you how to do it for the 2nd line try to do the same thing for the C E line (you know the correct answer) then say 4/3 and -3/4 are opposite reciprocal slopes, because when you multiply them, you get -1

36. anonymous

ten 4