Question

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.

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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 ?

Answer 7

yes

Answer 8

is the slope 1?

Answer 9

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

Answer 10

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

Answer 11

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)

Answer 12

I'm lost

Answer 13

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 ?

Answer 14

4

Answer 15

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?

Answer 16

3

Answer 17

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.

Answer 18

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

Answer 19

4/4

Answer 20

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 ?

Answer 21

sorry 3/4

Answer 22

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?

Answer 23

3/-4

Answer 24

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
\[ \frac{4}{3} \cdot - \frac{3}{4} \]?

Answer 25

i got 1/1 which is just 1

Answer 26

my bad forgot negative

Answer 27

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

Answer 28

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)

Answer 29

ok

Answer 30

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

Answer 31

okay its kinda starting to make sense

Answer 32

is that the final product

Answer 33

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

Answer 34

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

Answer 35

ten 4