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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.

find the slope of both lines

Find the slope for line BC first

Do you know how to do that?

Pick 2 points on the line

C and B?

Or you mean within the line?

within the line, i'll pick the first one
(1,1)

I suppose we can do (2,2) as well?

i don't think that's a point on the line

what are the coordinates for point B

oh wait you confused me.

(4,5)

Thats right

now we use the slope formula, rise/run

|dw:1432956614754:dw|

1 would be the slope?

wait, i think i did that wrong too.

4/3(?)

4/3 is correct

what would be the negative reciprocal of that?

I apologize, I have not had much time to rest so I see myself making a lot of mistakes.

-0.08(?)

you don't have to apologize, happens all the time

uhhh

ok, what is the reciprocal of 4/3?

i'm getting -0.0833333333 according to google for negative reciprocal.

and then the reciprocal would be 0.08. unless of course there's a formula i'm not remembering.

you don't need a calculator for this

Remind me how we determine it then if you would? Haha

|dw:1432956822160:dw|

.. -facepalm-
3/4
.75

now make it negative

so would it be the same case for negative reciprocal?
-3/4
-.75?

so we are looking at EF now?

yes. So do the same thing we did before

First find 2 points

f is -1,1, e is -5, 4.
just from that, i already know they are indeed perpendicular.

yep
(4-1)/(-5-(-1)) = -3/4

Is it that simple to answer the question? Oh my lord, I feel dumb.

once you understand it its simple, same with all math i guess