I need an answer check for my Math problem...sorry

[irwin]

I know I've asked a lot of math questions lately but I just need to make sure I've got this right because I'm so close to not passing the class. (Need a C- to pass; have 68.6%)

http://www.ezshots.com/members/passwird/images/passwird-9.jpg

I found one answer, but I don't know if there is more than one location for the fire.

First, I found the perpendicular bisector of Foster City and Belmont. Next, I constructed the angle bisector at the intersection of Hwy 92 and Hwy 101. The two rays intersect each other in the upper-right hand corner of the drawing. Are there more solutions?

http://www.ezshots.com/members/passwird/images/passwird-10.jpg

Thanks

[hapoo]

yeah thats right

[TheLoneGunman]

So, why isn't there an equivalent point on the lower left?

Just extend the map out and do the same thing, but go down instead of up.

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The Roof... the Roof.... The Roof is on fire... we don't need no water, let the mo'fo' burn! burn mo'fo' burn!

[irwin]

Originally posted by TheLoneGunman
So, why isn't there an equivalent point on the lower left?

Just extend the map out and do the same thing, but go down instead of up.


I thought about that, but the angle bisector of the 101/92 intersection doesnt intersect with the perpendicular bisector of the Belmont/Foster City segment when both rays are extended towards the bottom of the map. Or am I supposed to draw new lines somewhere? I'm confused now.

[TheLoneGunman]

Maybe I am totally confused, but if you used hwy 92 as a "hinge" you ought to be able to take your lines and simply draw them on the opposite side.

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We didn't start the fire... oh we didn't start...

[plutarcho]

If you draw a straight line between the two cities, the mid-point of that line would be equidistant from both the two cities and the two highways. If you draw a ray that extends outward from the intersection of the two highways to the upper righthand side, any house that resides along that ray would meet the two conditions (which as I read the question are separate, not joint). That is, just as far from one city as the other & just as far from one highway as the other.

But then again, I'm a little rusty on the old geo.

[irwin]

Originally posted by plutarcho
If you draw a straight line between the two cities, the mid-point of that line would be equidistant from both the two cities and the two highways. If you draw a ray that extends outward from the intersection of the two highways to the upper righthand side, any house that resides along that ray would meet the two conditions (which as I read the question are separate, not joint). That is, just as far from one city as the other & just as far from one highway as the other.

But then again, I'm a little rusty on the old geo.

Isn't that what I just drew? :)

[TheLoneGunman]

here is a tricky way to answer.

There are an INFINITE number of possible locations.

Reasons - a "roof" implies a third dimension. Therefore, if the burning location is 8ft tall, there is on x/y coordinate for it. On the other hand, if it is 12ft tall, then the x/y is slightly different. Since "Z" (height of roof) could be almost any number (including negative if location is in valley below sea level) then there are an infinite number of correct coordinates.

In a GPS system, you use THREE points to triangulate your position which only leaves two possible locations (and one is in outer space). However, this example only uses TWO which allows an infinite number of solutions for "Z"

[plutarcho]

I read your drawing to mean that the house is at the point where the two rays intersect. If so, you only have one point.

My not so elegant point is that the house can be at any point along my ray that bisects the origin(?) of the angle and the mid-point of the line connecting the two cities. Therefore, there are an infinite number of points (as mentioned in the previous post ;) )

If the two cities are the same distance from from the origin (or what ever you call it), then you can do the same with the lower left hand angle (South/West) by extending the ray in the other direction. But, if the cities are not the same distance, then this appears to be the only solution.

I wouldn't bank my grade on people like me!

[irwin]

Originally posted by plutarcho
I read your drawing to mean that the house is at the point where the two rays intersect. If so, you only have one point.

My not so elegant point is that the house can be at any point along my ray that bisects the origin(?) of the angle and the mid-point of the line connecting the two cities. Therefore, there are an infinite number of points (as mentioned in the previous post ;) )

If the two cities are the same distance from from the origin (or what ever you call it), then you can do the same with the lower left hand angle (South/West) by extending the ray in the other direction. But, if the cities are not the same distance, then this appears to be the only solution.


The cities are not the same distance from the origin :)

TLG, that's some deep thinking, I probably could impress the shit out of my teacher with that... or make myself look like a smart ass...

[plutarcho]

What coast are you on? It is after midnight here, shouldn't you be in bed?

:)

Good luck in your Math class.

[irwin]

Originally posted by plutarcho
What coast are you on? It is after midnight here, shouldn't you be in bed?

:)

Good luck in your Math class.

I'm on the west coast. Bay Area, CA. I'm always up late :) I always get the urge to check G|A every 20 mins or so hehe. I hope I pass Geometry. Math has never been my thing though, my 7th grade teacher reccomended that I stay in pre-algebra for a second year. FOOK. Now I'm behind all the smart kids.

[TheLoneGunman]

I think you should go with the 3-d solution.

The uniqueness of it should be worth some bonus points.

Further, if you aren't hoping for "suck up" points from your teacher, you will do better by showing something that obviously isn't copied from someone else (unless she reads Got|Apex).

[irwin]

Originally posted by TheLoneGunman
I think you should go with the 3-d solution.

The uniqueness of it should be worth some bonus points.

Further, if you aren't hoping for "suck up" points from your teacher, you will do better by showing something that obviously isn't copied from someone else (unless she reads Got|Apex).



Ok, TLG, I'll go for it in addition to the "normal thinker's" answer. I put it in my conclusion about the possibility of different answers. He'll probably return the papers back on monday so I'll let you know what grade you earned for me! :)

[CluelessSi]

Originally posted by TheLoneGunman
here is a tricky way to answer.

There are an INFINITE number of possible locations.

Reasons - a "roof" implies a third dimension. Therefore, if the burning location is 8ft tall, there is on x/y coordinate for it. On the other hand, if it is 12ft tall, then the x/y is slightly different. Since "Z" (height of roof) could be almost any number (including negative if location is in valley below sea level) then there are an infinite number of correct coordinates.

In a GPS system, you use THREE points to triangulate your position which only leaves two possible locations (and one is in outer space). However, this example only uses TWO which allows an infinite number of solutions for "Z"


haha fun answer accept for one big flaw... it is show on the map which is in 2-d .... eliminating the Z direction. but to answer your question. yes there is only one point on the map that can be the annswer and you have it right.

[TheLoneGunman]

My answer DOES work in 2-d. My claim is that it could be a 2 story house on 502 Main Street, a three story on 504 Main Street, a 4 story on 506 Main Street, etc.

i.e. They are not asking about a brush fire (which then refers to a 2-d point) but rather a ROOF fire which by its nature creates a 3-d component.

This would have had less than infinite solutions if they hadn't been so creative by mentioning the word roof.

If they said "car fire" then likely that would have had less answers too because although the height of a car is variable, the range is not nearly as great as a building.

[CluelessSi]

Originally posted by TheLoneGunman
My answer DOES work in 2-d. My claim is that it could be a 2 story house on 502 Main Street, a three story on 504 Main Street, a 4 story on 506 Main Street, etc.

i.e. They are not asking about a brush fire (which then refers to a 2-d point) but rather a ROOF fire which by its nature creates a 3-d component.

This would have had less than infinite solutions if they hadn't been so creative by mentioning the word roof.

If they said "car fire" then likely that would have had less answers too because although the height of a car is variable, the range is not nearly as great as a building.

But when they put it on a map then they assume variables like that are not signifacant because if that is signifacant then the city location has to be put into consideration (center of city?) and the road imperfections also has to be put into perspective.

the way u have it is that there is infinite points no matter what they give u just because a point has no dimensions thus there exists infinte points everywhere in space (Zeno's Paradox)


In conclusin your argument does not hold beacuse your point in the Z plane is still the same exact POINT on the 2 D plane.... it does not change at all in the 2D map no matter it be a 100 meter roof or a 2 meter roof.... The point on the map it self is the same being that it is a 2-d MAP! it is like looking down on the roof ... you can't tell how tall the roof is....
btw it has to be on the same location x/y the point that he has found the only variable is the z direction which in no way changes the x/y direction. with the intersecting lines only line that is equidistant is a straight line out of the page because you assume that the other points and lines are planes and lines thuse extend infinitly in the Z direction.


[Edited by CluelessSi on 06-07-2001 at 12:38 PM]

[TheLoneGunman]

Just like in school, I will continue to press the point.

A city has a definite "Z" (elevation) if it is not stated (that is why you see a sign at the edge that says "Population 40,000 elevation 200ft")

The roads also have a basically understood elevation.

[CluelessSi]

Originally posted by TheLoneGunman
Just like in school, I will continue to press the point.

A city has a definite "Z" (elevation) if it is not stated (that is why you see a sign at the edge that says "Population 40,000 elevation 200ft")

The roads also have a basically understood elevation.



but freaking on a 2D map it does not matter the third four and so on dimensions don't existe... (4+ being hyper and other factors like time and land movement and all sorts of things), at least on that map that does not state elevations. Thus u work the problem out on the 2-d with out the extra info.. One can argue infinite point on one point using Zeno's Paradox but why go there? those elevations are also estimates anyway...

[irwin]

Grade on assignment: 8/10 Damn. :(

There was another point where the roof fire could have started from. I should've bisected another angle created by the 101-92 intersection. I teacher apparently didn't care for the 3 dimension theory. Oh well...

http://www.ezshots.com/members/passwird/images/passwird-13.jpg