anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • anonymous
please help, i have 3 weeks untill i go to boot camp and i have to finish school.
phi
  • phi
can you "read off" the (x,y) coords for points B and C ?

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More answers

anonymous
  • anonymous
B (5, 4) C (1, 1)
phi
  • phi
ok on C for B, you want the "sideways" number (the x) first you did it backwards.
anonymous
  • anonymous
my bad, i havent always been real sharp in math, physics and space science are my thing
phi
  • 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 ?
anonymous
  • anonymous
yes
anonymous
  • anonymous
is the slope 1?
phi
  • 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 ?
anonymous
  • anonymous
so i would subtract 5 from 4? or the other way around
phi
  • 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)
anonymous
  • anonymous
I'm lost
phi
  • 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 ?
anonymous
  • anonymous
4
phi
  • 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?
anonymous
  • anonymous
3
phi
  • 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.
phi
  • phi
can you find the change in y from point F to pt E ?
anonymous
  • anonymous
4/4
phi
  • 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 ?
anonymous
  • anonymous
sorry 3/4
phi
  • 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?
anonymous
  • anonymous
3/-4
phi
  • 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 \[ \frac{4}{3} \cdot - \frac{3}{4} \]?
anonymous
  • anonymous
i got 1/1 which is just 1
anonymous
  • anonymous
my bad forgot negative
phi
  • phi
I would write it this way: multiply top times top and bottom times bottom \[ \frac{4}{3} \cdot - \frac{3}{4}= - \frac{12}{12} = -1\]
phi
  • 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)
anonymous
  • anonymous
ok
phi
  • 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
anonymous
  • anonymous
okay its kinda starting to make sense
anonymous
  • anonymous
is that the final product
anonymous
  • anonymous
you can have your medal back when you come back...
phi
  • 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
anonymous
  • anonymous
ten 4

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