For example, if i was my own student in my class:
Triangle ABC's:
orthocenter (x, y)
Euler Line: y = mx + b
Triangle DEF's:
centroid (x, y)
circumcenter (x, y)
orthocenter (x, y)
Euler Line: y = mx + b
#5.3
- post your conclusion to I.5.3.2
- copy down the bold faced definitions on pg. 238
- perform I.5.3.3
- post your conclusion to I.5.3.3
- (1-18) all
posted by msichan @ 12:32 PM
30 Comments:
Whee. Section 5.3's conjecture was rather simple.
Conjecture 31: In a triangle, the longest side is opposite the angle with greatest measure and the shortest side is opposite the angle with least measure. XD;;
I would type out my work from last night, but I have to re-do and re-check everything. And fold the laundry. *facepalm*
Sincerely,
--Mary.
Here's wat i got for the triangles:
Triangle ABC:
Orthocenter:(-3/5, -23/5)
Euler Line: y=-38/115x+807/17
Triangle DEF:
Centroid: (-3,-11/3)
Circumcenter: (-37/2,49/2)
Orthocenter: (28,-60)
Euler Line: y=-169/93-848/93
I'm not to sure about the Euler Line for my Triangle DEF so im going to check it tonite.
I agree completely with your conjecture Mary
Gyaah. Here's another quickie before I'm trapped in a land of tee-shirts and underwear. X_x;
Conjecture 32: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
And yaaay! XD British, you're like the Algebra-Guru of my life. I shall forever and eternally seek your guidance. I'm so friggin' glad you posted your answer early so now I have a reference for later when I re-do my work. XD
Sincerely,
--Mary.
For the orthocener of ABC I got really crazy points.
(7/4, 3/4) ???? I tried Ms. Chans thing when I didnt want to work with fractions but I dont think I did it right!
keenan,
show your work. defend your answer. maybe someone can figure out where you went wrong (assuming that you are wrong).
ABC -
orthocenter - ( -3/5, -23/5)
euler line - y = 19/23x - 1/32
DEF -
centroid - (-3, -22/3)
circumcenter- (-6, 49)
orthocenter- (-271/-43, -39/43)
euler line - 169/9x - 49/1
ok most likely i probably made a mistake somewhere and got the answers wrong, but i went over it a million times and i still dont see anything wrong that i did.
but probably tomorrow ill see what i did wrong.
gosh this makes me feel stupid =/
if i finish my homework in time ill try to explain how i did mines, incase someone sees if i did something wrong and can maybe help me.
I have a question.... When you multiply an equation to get rid of all the fractions at the end u have divide by that # right????
ie: For the orthocenter here is my work. This is Vertex A but line BC
I got to y-6= -1/4(x-5)
To get rid of the fraction I multiplied by 4 and got
Do I divide by four?? If so when??
hey i need to know who will be at my home on sunday at 12:00 for our "study group". there will be pizza and soda if anyone is concerned ( andres i have coffee but no cookies sorry.) there should be at least be one GIRL i think my DAD would freak if i was in a house full of BOYS!!! again i need to know who will be there so i can give you directions.
Bwee. XD
Before I post my results, I've got to finish a few more calculations. Although, I do have a question about your circumcenter, Dana. How did you get the coordinates (-6, 49)? *headscratch*
I agree with British. I also got (-37/2, 49/2) as my coordinates.
I found the perpendicular bisectors for DE and EF.
DE:
Midpoint: (1,-3/2)
Perpendicular Slope: -4/3
y + 3/2 = -4/3(x-1)
y + 3/2 = -4/3x +4/3
y + 3/2- 3/2= -4/3x +4/3- 3/2
y= -4/3x - 1/6
EF:
Midpoint: (-8,-7)
Perpendicular Slope: -3
y+7 = -3(x+8)
y+7 = -3x-24
y+7-7 = -3x-24-7
y=-3x-31
Finding the circumcenter:
-4/3x - 1/6 = -3x - 31
-4/3x + 4/3 - 1/6 = -3x +4/3x -31
-1/6 = -5/3x-31
-1/6 + 31 = -5/3x-31+31
-185/6 = -5/3x
(-3/5)-185/6 = -5/3x(-3/5)
-37/2=x
Plug x into y:
y= -3(-37/2) -31
y= 111/2 -31
y= 49/2
I plugged these variables into both of my perpendicular bisectors and my equations have been true.
Sincerely,
--Mary.
Triangle ABC:
centroid (4,-10/3)
circumcenter (63/10,-27/10)
orthocenter (-3/5, -23/5)
Euler line:
y=19/23x-75.3/8
Triangle DEF:
centroid (-3,-11/3)
Circumcenter (15/2,-107/2)
orthocenter (28,-60)
Euler Line:
y=169/3/31x-4912/3/31
I dont understand the instructions for any of tonites homework. Can someone help me?
Okie dokies!
These are my answers. Though I do need a bit of help on finding the equation of the Euler Line. I know you have to choose two of the three points of concurrency that falls on the Euler line, find their slope, and plug one of those two points and that slope into point-slope form.
[Ahahaha! XD This sounds like a tongue-twister. "...find their slope, and plug one of those two points and that slope into point slope-form."
Findtheirslopeandplugoneof thosetwopoiintsintopoint-slopeform!
XDDD!!! ...*cough* Erm. Yeah. Sorry. x__X;]
Can someone show me their work for finding their Euler Line so I can follow it as an example? I have trouble finding the slopes when there are fractions everywhere. >.<; I have trouble knowing when to multiply to make them whole numbers and when not to...[Which is probably why I loved constructions so much. XD No numbers involved. Ahahaaa.]
Thank you very much in advance. ^-^ I'd really, really be humble to your help.
Triangle ABC--
Orthocenter: (-3/5, -23/5)
Euler Line: Finishing it up right now after section 5.3.
Triangle DEF--
Centroid: (3, -11/3)
Circumcenter: (-37/2, 49/2)
Orthocenter: (28, -60)
Euler Line: Finishing it up now after section 5.3. [Yes, I have strange work ethics sometimes. XD]
I plugged each of the coordinates into my perpendicular bisector and altitude equations; I'm pretty confident they're true considering I re-checked them. My belief is reinforced since I share the same answers as British and I think I've made it evident I trust his judgment--especially algebraically. XD;; [...Now, if only he was a good friend and didn't ditch a certain someone on a a certain eighth grade field trip to Islands of Adventure!]
Sincerely,
--Mary.
keenan,
if your eqn is y-6= -1/4(x-5), then multiply both sides by 4 to get:
4y-24 = -1(x-5)
4y-24 = -x + 5
4y = -x + 29
divide everthing by 4 now to get:
y = -1/4 x + 29/4
mary,
you can do fractions if you just allow yourself to believe. i have faith in you.
see my earlier posting to keenan regarding how to handle fractions....
hey i need to know who will be at my home on sunday at 12:00 for our "study group". there will be pizza and soda if anyone is concerned ( andres i have coffee but no cookies sorry.) there should be at least be one GIRL i think my DAD would freak if i was in a house full of BOYS!!! again i need to know who will be there so i can give you directions.
Ack! Jessica, I didn't ask my Mommy and Daddy yet. I'll ask my Mommy when she comes home from work so she can convince my Daddy to let me go...XD I went on mapquest and searched the directions from my house to your's. I'm not sure if my Papa will be happy driving! XDD Caaarpoool, please.
So, Sunday? Gyaah. Pity we can't meet earlier...there's going to be FCAT on Monday, so we won't be able to stay long at your house. Hmm. Are Dana, Peuandro, Andres, and Nick going? I know Keenan said he can't. [SeaWorld. XD Lucky, little...]
Maybe I can just not go to that Quincenera [however you Spanish people spell it! XD] on Saturday. Not that I'll be able to communicate with anyone fluently anyway! XDDD;;; *facepalm*
I can probably volunteer my humble abode for the next-next meeting. XD
Sincerely,
--Mary.
i got my extra credit!
I 5.3.2
c-31 in a triangle, the greatest angle is opposite the greatest side, the second greatest angle is opposite the second greatest side and the least angle is opposite the least side.
I 5.3.3
c-32 the measure of an exterior angle of a triangle is equal to the 2 remote interior angles.
im doing my triangle DEF over...and just so i dnt get started off incorrectly here are my midpoints snd slopes...can some1 verify w/ me PLEASE...because 2day i made alot of careless mistakes:
DE-
mdpt (1,3/2)
perp m -4/3
EF-
mdpt(-8,-7)
perp m -1/3
FD-
mdpt (-2,-5/2)
and perp m 18/11????
correct me if im wrong!
ok wow...umm i have:
Triangle ABC:
Orthocenter:(-3/5, -23/5)
Euler Line: y= 19/69x-102/23
&
Triangle DEF:
Centroid: (-3,-11/3)
Circumcenter:(-197/2,361)
Orthocenter: (497/26, -591/13)
Euler Line: y=-2102/955x-8407/955
yeah i have a big feeling im wrong lol..but we'll see tomorrow lol
for Triangle ABC:
orthocenter (-3/5, -23/5)
Euler line y = 19/69x-102/23
Triangle DEF
centroid (-3, -11/3)
circumcenter (19/2, 77/6)
orthocente-M.I.A
Euler line y = 11/5x + 44/15
Hee. Hiya, Robyn! ^-^
You've got most of them correct. For a few, you just left off a negative sign and such.
DE:
Midpoint: (1, -3/2)
Perpendicular Slope: -4/3
EF:
Midpoint: (-8,-7)
Perpendicular Slope: -3
DF:
Midpoint: (-2, -5/2)
Perpendicular Slope: -18/11
Sincerely,
--Mary.
P.S. Ahahaha! XD Nice one, Nick! "Missing in action"?! XDDD I gotta use that sometime.
okay im doing my euler's line forr triangle ABC..u have 2 find the slope first right?....well right now im stuck at:
-19/30
------- (fraction, lol)
-23/10
HELLLPPPPPP!!!!!
thanks mary! but um for line ef woulddnt the perp m be -1/3 because i got the slope -2/-6 which equals +3..so shouldnt the perp slope be -1/3???
Hee. You're welcome. ^-^ Ack. Rob, I don't think -2/-6 equals 3. XD It would equal 1/3.
How did you get -2/-6?
-6-(-8)=2
-5-(-11)=6
2/6 equals 1/3. So -3 would be perpendicular to 1/3.
Sincerely,
--Mary.
Conjecture 31: In a triangle, the largest side is opposite the greatest angle and the smallest side is opposite the angle w/ the least measure.
Conjecture 32: The measure of an exterior angle of a triangle is equal to the sum of the remote interior angles.
I finished the conjectures first 2 get them over with and I'm finishing my centers for (DEF).
This is wat i got for Triangle ABC:
Orthocenter:(-3/5, -23/5)
Euler Line:
y=19/69x + 408/9
I might be off with this Euler Line because I had trouble figuring out the slope of the eq.
oops! it was just another careless mistake that i looked over just like *snap* that! _hiding my face_ thats kind of embarassing...thanks though.
C-31: In a triangle, the longest side is opposite the largest angle, the second largest side is oppostite the second largest angle, and the smallest side is opposite the smallest angle.
C-32: The measure of an exterior angle of a triangle, is equal to the sum of the 2 remote interior angles.
P.S. yes mary, the coordinates are "missing in action". lol!!
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