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.

- anonymous

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- anonymous

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- anonymous

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

- phi

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

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## More answers

- anonymous

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

- phi

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

- anonymous

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

- 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

yes

- anonymous

is the slope 1?

- 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

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

- 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

I'm lost

- 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

4

- 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

3

- 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

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

- anonymous

4/4

- 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

sorry 3/4

- 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

3/-4

- 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

i got 1/1 which is just 1

- anonymous

my bad forgot negative

- 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

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

ok

- 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

okay its kinda starting to make sense

- anonymous

is that the final product

- anonymous

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

- 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

ten 4

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