Congratulations, Geometry Honors!
I am soooooooooo PROUD of you guys for finally using the blog for which it was intended to be used! You have officially raised yourselves into the "Honors" category. No longer are you guys "wannabe Honors students". You are communicating with each other, sharing answers, and asking questions. i cannot tell you how extremely HAPPY that makes me. Keep it up!
#4.6 Intersection of Lines
- finish I 4.6
- If triangle TRY has coordinates T(a, d), R(b, e), and Y(c, f), then the centroid has coordinates ---?---
- (1-11) all
- (13-14)
have a question?
post a comment.
posted by msichan @ 9:23 AM
74 Comments:
Alrite Guys.... We got her happy.... We cant let her down...... Ready...... Set...... BLOG!!!!!!!!!!!!!!!!
YES! TO WHAT KEENAN SAID.
having ms. chan being happy takes off alot of pressure lol.
hopefully we get to do the construction test at home.
im going to keep praying that she does.........
-
Dana
02/15/07--
Yaaay! XD We wuuuuve yoo, tooo Ms. Chaaaan. *dancedance* Ditto to Keenan and Dana. This blog is ten kinds of mega-useful; it's a bit fun actually, if you think about it. XD;; We get to chat with a lot of people from our class while helping each other with homework. ...Let's all have one big-web-hug? XDDD
And yikes! I've been dreading the construction test all week. >.<;; If I want to be accurate, I take like--at least ten or fifteen minutes for each construction! *cries* I'd never have enough time if it was during class.
So, Dana. XD You're not the only one praying. Well, homework time! Nick, if you're reading this, which question did you need again? ^-^
Sincerely,
--Mary.
P.S. Yikes. I took a quick glance at the word problems. XD;; ...I feel squeamish!
ok so for the investigation, for example to find the midpoint of line AB you use the formula y2-y1/2, x1-x2/2 rite?
well i tried using that formula and the midpoint that i got were different from the ones ms chan did on the overhead.
can someone please help, i just need to no what formula to use and once i get the answer do i use these #s as my midpoint or are there more steps to do.
im sorry if im asking too much. its just that i dont really get this =[
thank you
-
Dana
Ooh! Dana, to find the midpoint of line AB, you don't subtract. To find the midpoint, you add.
So the formula for finding the midpoint would be:
(x1+x2)/2
(y1+y2)/2
I know we talked about the whole y1 and y2 thing at the library in the morning, but the order that you add doesn't really matter. XD
Sincerely,
--Mary.
o so thats why it wasnt working for me.
thanks mary, your awesome!
ok so even if the formula says to subtract you still add rite?
well thanks again!
-
Dana
4.5 # 32. thank you mary!!!
You're welcome, Dana. ^-^
And, gyaah. Thank you. XD I'm honored you think highly of me. Erm. Although, I'm not really sure of what you mean by "even if the formula says to subtract you still add".
Hmm. I think I know what you're trying to say, though. Let me just use an example.
Let's say you need to find the midpoints of:
(5, 6) and (3, -2)
You know to find the midpoint, you refer to:
(x1+x2)/2
(y1+y2)/2
Let's start with the "x".
(5+3)/2 = 8/2 = 4.
So you add. But if you're dealing with negative numbers like in the y-coordinates of these two points:
6 and -2. Adding 6+(-2) is the same as saying 6-2; that's why sometimes Ms.Chan will subtract rather than add on the overhead because it's accomplishing the same thing; you still get the same answer if you add 6 and -2 [4] or subtract 2 from 6 [4].
Is that what you're wondering about?
Sincerely,
--Mary.
ya thats what i mean. it makes much more sense now.
thank you again so much
=]
your so nice!
You're welcome, Nick. XD Okie dokies. Here's what I had done.
Section 4.5: #32--
The question asks you to "find the equation of the line containing altitude HT."
First things first. XD Remember the points: W (0,0) H (8,3) Y (2,9). Sketch yourself a vague picture so you can imagine where you need to get the altitude.
[Please ignore my lack of paint skills. XD]
http://tinyurl.com/2duarm <--Copy and paste.
Okie dokies. What is the definition of an altitude? You know that is has to create a 90-degree angle and starts from the vertex and ends at the other side.
Since you need to find HT, your vertex would be H and the side the altitude has to cross is WY. And since an altitude creates a 90-degree angle, you'll want to find a line perpendicular to WY.
http://tinyurl.com/yvenel <--Copy and paste again. XD
First, find the slope of WY:
Delta Y/Delta X.
W (0,0) Y (2,9)
9-0 over 2-0= 9/2.
But you want to be perpendicular to WY's slope, so make it into a negative reciprocal. The slope you want HT to have is -2/9.
You want to make an altitude from H. H's coordinates are (8,3). You have a point and a slope now. So just use point-slope form to find the equation you need! ^-^
y-y1=m(x-x1)
y-3= -2/9(x-8)
Solve it and you should get:
y= -2/9 + 43/9. If you still need any help on getting that answer, don't hesitate to ask. ^-^
Sincerely,
--Mary.
Hmm.
I think I've got the conjecture. But this is one of the more complex ones to comprehend so far, in my opinion. Though. I do think I understand it, but since I'm albeit uncertain. I'd appreciate any help. Many thank yous in advance. ^-^
Conjecture 24:
If triangle TRY has coordinates T(a, d), R(b, e), and Y(c, f), then the centroid has coordinates :
(a + b + c/3, d + e + f/3).
Can you guys see where I'm coming from? Does it make sense, or should I elaborate a bit more...?
Sincerely,
--Mary.
mary, you basically got what i got. i dont think you can really elaborate it more. its pretty good the way it is......or alteast i think it is.
-
Dana
thanks for the help mary!! im going to try it when i am done with tonights homework, to see if i understand.
help is greatly needed!!!.... 2-4 on tonights homework!!
hey mary, for number 32 (the one you were helping me on) i got -47/9 not 43/9.
I dont get #4 or 5 on tonite's homework
testing
ms. chan what do u mean by testing?
hey is the that hard and long? I just got home. :(
nothing, dana. i was just testing out the time stamp on the posts to see if it was accurate. just ignore it.
arghhhhh! I forgot to put the word HOMEWORK! Sorry, blonde moment.
im sorry im not going to try to ask any more questions, im probably bothering you guys, but i really need help on #9 for 4.6.
i really need to no how to do it or what formula it is because alot of the questions are like this one so i really need to no it.
i took all the notes in class but i still cant comprehend how its supposed to be done. i feel really stupid.
i would really really really really appreciate if someone can help me.
pretty please!!!
thanks
-
Dana
Aaaaaaaa Is Kinda Late To Start Homework !!!
Awwww How Cute! Dana Doenst Wanna Bother By Asking Questions, You Shouldnt Worry About It Because This Is What This Blog Is For =) Let Me See If I Can Help Since Im Gonna Start Doing It Now
Hmm. Hello everyone. ^-^
I think there's something wrong with me. XD I just randomly passed out while I was doing my homework! Either I'm abnormal and need to see a doctor about fatigue or I was just sleepy today. ....XD;;
I'm having a bit of trouble in my homework. [Well, bit is a bit of an understatement here, but in about a few minutes, I'm going to go bald from tearing out my hair.]
Number Five:
Okie dokies. I can kind of see what I need to do. When it says "formed by the x-axis, the y-axis, and the line", I see that line running through both the x and y axis and whatever two points the line intersects along with the origin would form the triangle.
I already attempted this after changing the line equation from standard to slope-intercept form, and while I did form a triangle, when I used the conjecture to find the centroid, my centroid was on a side. And you can't have a center of gravity on the side! *sigh*
Numbers Six through Eight:
I feel so inept. For each of these problems, I was to locate the centroid, but how can I locate the orthocenter and the circumcenter using equations? If I found all three altitudes on each side and all three perpendicular bisectors on each side, what would I do then? Would I "average" those points out,too? I really don't want to start graphing because I really want to try getting this using Algebra.
And Nick, I'm pretty sure the answer should be 43/9. Can anyone verify that for me? And, Nick, how did you end up with -47/9?
I'd really appreciate the help--dude, I'll think you're the most mega-rad-awesome person aliiiiive. XD *clings to your ankles!*
Working on number nine right now. ^-^ I'm going to stop stressing on those last four problems for a bit.
Sincerely,
--Mary.
lol andrea.
it would be so great though if you can be able to help me if not we'll just try to go over it tomorrow when we get into our groups.
by the way thanks =]
yay!! im on section 4.3 and its fianlly easy!! i was getting tired of all that constriction stuff...oooo my dear beloved algebra. how i missed you. but yeah anyways i guess im goiong to be running through these sections now. hopefully if i stay on task i'll get it all done. so yeah ok im going back to my work. be back soon
hey um for the investigation do we have 2 graph ALL FOUR triangles on the SAME graph?
umm..i feel kinda embarassed..umm i don't remember how you would do number 5 of 4.3...umm can someone help me??
Ack! No, Robyn. XD
I tried that. If you graph them all on the same coordinate plane, some lines are going to overrun each other, so you should do them in separate small graphs rather than one big one. ^-^
...Hiii, Robyn! XD *wavewave*
Sincerely,
--Mary.
im sorry mary, i wouldve loved to help you after all you have done for me but i dont no what im doing.
for #6-8 i was able to find the centroid but i dont no how to find the circumcenter and the orthocenter.
and for #5 o my frickin god i dont even no what to do on that one. i understand wt their saying but i just cant figure out what how to do it.
i dont no whats wrong with me its probably because i havent slept much the this week and my brain is so tired i cant focus on anything. its sad. im just stupid i guess lol.
maybe we can try to go over it tomorrow in the library see if we can figure it out.
Hey, Andres. ^-^
I think I posted a comment about that problem a few days ago. Hmm. Let me check...and here it is! I'll just copy and paste my explanation.
"Number Five: Section 4.3
Okie dokies. It's asking you to find the coordinates of the other endpoint. They give you the endpoint [12, -8] of a segment to the midpoint [3, 18]. So visually:
Point A--(12,-8)
Point B--(3,18)
.A------.B------[?]
You're trying to determine the question mark. The other endpoint.
The formula to locate a midpoint as you know is:
(x1+x2/2, y1+y2/2)
Do find the other endpoint, plug in the information you already have!
Remember, the given endpoint is (12, -8) and the midpoint is (3, 18).
So. Let's start by finding the "x" of the other endpoint.
12+x/2=3
12 is x1, "x" is x2. They would equal three, because the "x" of the midpoint is 3. ^-^
After you set that up, just multiply it both sides by two to get:
12+x=6.
Subtract 12 from both sides:
12-12+x=6-12
To get:
x=-6
Now you know the "x" for the other midpoint. Hee. Just follow the same format for "y". To get you started, just solve this:
-8+y/2=18."
If you still need some confirmation, don't hesitate to ask! British also found another way to do it, if you go read the comments. ^-^
Sincerely,
--Mary.
hey mary for numbers 6-8 i think you can use algebra. if you recall what ms chan went over the other day in 4.5, she gave us the out-line on how to find the perpendicular bisector. but i think it was only for one side. so maybe here you would have to do it three times. which i think there would be a simpler way to do it. but i don't know. ANY THOUGHTS??
And robin, you are supposed to graph each triangle seperately. NOT all on the same graph. but on the same graph paper.
oh nvm. i just checked the blog from before so yeah i got it.
yes thanks mary. your the bestestest lol
THANKS!!!!!!
I don't understand how you got the conjecture. I'm also not sure if I understand the homework very well
Ack! Dana, Dana, Dana. XD Buddy, you don't need to apologize. And besides, you've helped me too, you know! It's all okie dokies. XDDD *headpatpat* So don't worry about it. And yeah! We can toe-tay-lay go over it tomorrow morning. We should do a quick review on constructions too.
And if we can't solve this problem, we can always go over to number five's house and assassinate it. XD;; Gyaaah! I think my brain cells are dying. XDDD But thank you Dana for the reply, Dana. You and I are floating on the same boat.
Sincerely,
--Mary.
P.S. Ooh, I know, Nick. Butbut. There has to be an easier way! I don't wanna do all of that. D'x *cries* OOH. I KNOW. HOW ABOUT. SOME PEOPLE DO SIX, SOME DO SEVEN, AND SOME DO EIGHT AND IF THERE IS A PATTERN FOR EACH QUESTION, WE CAN ALL SHARE OUR ANSWERS AND GET THE RIGHT ONE. XD Eeeeh? Eeeeeeh? It'll save time for aaaall of us! *strikes a pose!*
You're welcome, Andres. ^-^
And I might be wrong Elisa, so don't take my word for it. What did you guys get for conjectures?
HEY UM...WHAT DID U GUYS GET 4 #1...? i GOT Y=20/3 SO FAR..BUT I ALREADY THINK IM WRONG...
This comment has been removed by the author.
So... ummm how is everyone doing....Ummmm I need help with # 1 please... How do I find the exact points????????
Wowwies. XD We hit the forty-comment mark. Woo-hoo~. *dancedance* Ceeel-aah-bray-shun time, c'mon! *moonwalks*
Hmm. Robyn, they're asking you to find the point of intersection of the two lines. What did you get to do to find that answer? You need to find the coordinates, Robyn.
The two equations are:
y=3x+5 and y= -6+10.
To help you get started, solve this:
3x+5 = -6+10. After you find the value of x, substitute it for one of the equations to find what y equals. Then you'll have an x and y coordinate. ^-^
Sincerely,
--Mary.
THANX MARY! I FREAKING LOVE U! LOL
Ack! My mistake. I forgot the variable x after -6. Don't forget that. XD;;
Equations:
y=3x+5 and y= -6xx+10.
To find the x-coordinate of intersection:
3x+5 = -6x+10
Sincerely,
--Mary.
SOOOO...I ENDED UP WITH X=-1/3 AND Y=4...? is it right? *crossing fingers*
Mary I am starting to understand # 1 now.... letrs see what happens
[XD! I wuve you too, Robyn!]
Hmm. Did you graph the two lines? If you do that, you can see where the two lines intersect; when you can see that, you should try to aim for that answer when doing the equations.
Can you type out your mathematics so I can see how you came to that answer? That way if you had accidentally had a miscalculation, I can help you find it. ^-^
Sincerely,
--Mary.
3x+5=-6...woah i just noticed ur ttypo...
:'( ill try again..
Hey guys, iv'e been reading most of these comments(44!!!!!), does anyone have at least a clue in what direction I should go for #5?
-Thanks in advance
-Javi
can i also ask 4 some advice on #'s 6,7,8......(the entire 5-11). lol! im just kidding.
Is there anyway we can use algebra for the points of concurrency (orthocenter... blah blah) without taking up 20 pages of work.
yes im still stuck on number 1
but b4 i move on.....mary does x=5/9???
i got that like this..
3x+5=-6x+10
+6x +6
9x+5=10
-5 -5
9x=5
x=5/9
Yes! Robyn, you got it right! XD I also got that for "x" and after I found "y", I plugged it in for both equations and they worked. ^-^
Javi, I don't know what I can say you help you, because I'm just a stick in the mud when it comes to those problems. I'd really appreciate some advice, too. XD Please and thaaank you! I kind of gave a vague idea earlier for number five, Javi. I have the "I know what I want to do, but how can I do it" cloud suffocating me right now. e.e;; Heeelp. XD
Sincerely,
--Mary.
P.S. Wowwies. Fifty-comment mark. XD ...Wooaah. Wicked.
yay! okay thennn y=20?!?!
eyez closed
crossing fingerz
Aaaah. XD Robyn, can you show me your work that you used to solve "y"? Actually, try plugging in the variables to see if your equations are true or not.
It would also help to graph those lines to see an estimation of where they should intersect:
[Please ignore my non-existent paint skills.]
http://tinyurl.com/26mmnt <--Copy and paste.
The pinkish line is y= -6x+10. The purplie one is y= 3x+5.
The graph would be the estimation; the equations will help you find the exact point.
Sincerely,
--Mary.
I dont get 4.6.... I dont get # 1.... Someone please help..... Please I dont know how long I can do this.
yeah random post. so yeah im on number 26 of the 4.3 humber. yes im still on 4.3. yes im very sorry..i should die but im not going to.. so yeah umm i think we could go to 100 posts! whos with me!!!?
NOOOO SOMEONE HELP ME BEFORE MR. STUPID ANDRES
keenan, thats the same problem that im stuck on. i have no idea what the steps of doing this are. i think we should really go over that problem in the library tomorrow or we can go over the constructions on ch.3 cause i feel a test coming up =/. so im sorry i cant help.
o and andres im totally with you. it would be so awesome if we can get to a 100! lol
yeah thats what my graph looks like...but what does y equal?
Dana what a great idea.... We will go over homework in the library. SOUNDS GREAT!!! Well as for me I got other homework to attend to..... hopefully we'll understand it after some much needed bed rest.
what time in the library???? because i need serious HELP!!!!!!!!!!!
how do u find #2?
On 4.6 For #1 I Substituted What Y Is Equal In The Other Equation. So It Looks Like
-6x + 10 = 3x + 5
- 5 - 5
-6x + 5 = 3x
Divide Everything By 3 To Get x By Itself...
And It Gives Me
-6/3 + 5/3 = 3/3x
Meaning:
-2 + 5/3 = x
Then I Pluged It In The Original Equation And I Dont Know Is Wierd
ARRRGGG IM STILL ON 26...im brain dead right now. i was doing so well intil i got here..and i still have to try and get all caught up in the class...i just hope we don't have a notebook check this week.
Ack. XD Up to one hundred posts? Bwahaahaa. Can we spam? Hmm. Who's still awake and online, by the way? I can explain number one if anyone's still here--or number twenty-six. XD Ahahaha.
I just don't want to babble too much if I'm alone. XD Gyaaah. OH. GAWD. I DIDN'T FINISH ENGLISH HOMEWORK! Keeenaaaaan! We just had those two stories with those Brothers andand that swimming kid, right?
Sincerely,
--Mary.
ugh!!!! im frustrated. im like still on number 1. mary whats the earliest u can meet me at school 2 help me with ALLLL of this?
ok i skipped 26 and on 27...i feel very lazy now though...grr...im soo tired...
IM STILL ONLINE!
can u please help me with #1
omg ur so awesome mary
what would our class do without u?
=]
Aaaaaaaaa The Homework Is So Complicated!!
Alright, Robyn. I'm usually at the library with Dana, Andres, and Keenan around seven-seven ten-ish until seven-thirty. ^-^ So you can meet us there and we can talk about it. But, if you're still awake, I can explain number one to you.
Number One:
Okie dokies. You have to graph the two lines: y= -6x+10 and y= 3x+5.
By doing so, you get this: http://tinyurl.com/26mmnt <--Copy and paste.
The question says to estimate the point of intersection; from my personal opinion, it looks roughly about at:
(1/2, 13/2) [13/2=6 1/2]
To solve both equations, you have to find at least a value from one of the variables, in this case "x". So set up your intersection equation:
3x + 5 = -6x + 10.
Since 3x and -6x are like terms, you can add, subtract, blahblah with them. I'm going to add -6x to both sides:
3x+6x+5= -6x+6x+10
9x + 5 = 10.
To isolate 9x, subtract 5 from both sides:
9x + 5 - 5=10-5.
9x = 5
Divide 9 from both sides; x=5/9.
Now, plug that into one of your equations:
I'm going to plug "x" into y=3x+5.
y=3 (5/9) + 5
y= 15/9 +5.
To add fractions, they must have common denominators. So 5/1 turns into 45/9.
y= 15/9 + 45/9.
y=60/9.
Now to check your work:
y= -6x + 10.
60/9 = -6(5/9) +10. It should come out to be true.
If you still need some elaboration, don't hesitate to ask, Robyn. ^-^
Sincerely,
--Mary.
thanks! i get it now...but now i need help on #2 :'( give me steps PLEASE not the answer
:'( i guess u guys went 2 sleep.
so ill c u all n the library 1st thing n the morning.
ok i skipped through some of 4.3 so i might need some help with it. so yeah..i feel so dumb right now...i have all this work and its taking forever to get it.
pray for me
get it done*
i get it, its jsut taking forever for me to get all the work done
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