a damn question (2 Viewers)

[littleboy]

If AB is the diameter of a circle and P another point on the circumference then Euclidean geometry tells us that angle APB = 90 degrees.
Use this fact to show that the equation of the cricle whose diameter has endpoints A (j,k) and B (m,n) is

(x-j)(x-m) + (y-k)(y-n) = 0

thanks

 

[magician]

Perhaps, (not sure if this works, I haven't checked it), make P point (x,y), then somehow you need to find the eqn of circle, so you need centre and radius of circle to be known. So an idea I have (like I said, I don't know if this works, I haven't tried it!) find length AB, midpoint should be the centre of cirlce then half of the length should be the radius. Hence, put it into the general form of circle and solve?

Hope this helps, otherwise if it doesn't, someone else may be able to answer you question on this thread- Anyone else out there have any ideas? Sorry if this doesn't work, it was just an idea I had when I read your question!!!

Good luck!

 

[magician]

Wait, just realised I ignored the info about 90 degrees- ah damn, so my idea doesn't answer your question!!! Mabye somehow pythagorean rule comes into it? Lol- someone else is now free to answer!!!!

 

[FinalFantasy]

let P(x,y)...
Gradient PB=-1\Gradient PA
(x-m)\(y-n)=-1\[(x-j)\(y-k)]
(x-m)\(y-n)=-[(y-k)\(x-j)]
times it out u get
(x-j)(x-m)+(y-k)(y-n)=0

 

[~ ReNcH ~]

(x-y)(x-m)+(y-k)(y-n)=0

(x-j)(x-m)+(y-k)(y-n)=0

...just to avoid confusion...

 

[FinalFantasy]

oops hahaha, lemme fix it =P

 

[Templar]

then Euclidean geometry tells us that angle APB = 90 degrees.

Is that the exact wording of the question? Quite strange to use the phrase Euclidean geometry.

 

[Archman]

Is that the exact wording of the question? Quite strange to use the phrase Euclidean geometry.

What's wrong with it?

 

[Templar]

What's wrong with it?

OK, planes with Gaussian curvature of 0 does get boring eventually, but anything else would be overkill in the HSC, at least in my opinion. Not to you, but certainly to a lot of other people.

Anyway, isn't it assumed knowledge that Euclidean geometry is the only geometry taught in the HSC?

 

[Trev]

Anyway, isn't it assumed knowledge that Euclidean geometry is the only geometry taught in the HSC?

mm theres diff types of geo?...circle or plane? thats the extent of my geo knowledge heh, i didnt kno they had diff names

 

[Archman]

OK, planes with Gaussian curvature of 0 does get boring eventually, but anything else would be overkill in the HSC, at least in my opinion. Not to you, but certainly to a lot of other people.

Anyway, isn't it assumed knowledge that Euclidean geometry is the only geometry taught in the HSC?

...er you still havent answered why it's wrong to use the terms "Euclidean geometry" in this instance here. Using Euclidean geometry just means that the implied bit can be worked out using the methods such as angle chasing etc, not algebraic bashing.

Btw its a lot less boring than what you think, a lot of the other geometry (not all), just eventually tend towards algebra, so hence losing the "geometric niceness" (i made that term up)

In fact, you are in no position of commenting on its boringness, with the amount you know.

Just ask laurie if you disagree.

 

[Templar]

In fact, you are in no position of commenting on its boringness, with the amount you know.

Just ask laurie if you disagree.

True.

Sadly Laurie refuses any discussion with me since it just goes on and on and on and...

And I don't know whether I'll see him again before uni.

Alright I'm stupid, you and Laurie are smart, I said more than I was qualified to. End of point.

 

[Slidey]

mm theres diff types of geo?...circle or plane? thats the extent of my geo knowledge heh, i didnt kno they had diff names

Affine geometry, projective geometry, et cetera.

Euclid's axioms were half-intuitive, half-rigourous. As such, some of them can be replaced to form new and interesting non-Euclidean geometries.

Oh, and circle geometry is a subset of plane geometry, not a different geometry.

 

[Trev]

Affine geometry, projective geometry, et cetera.

Euclid's axioms were half-intuitive, half-rigourous. As such, some of them can be replaced to form new and interesting non-Euclidean geometries.

Oh, and circle geometry is a subset of plane geometry, not a different geometry.

yes........

 

[Captain pi]

Affine geometry, projective geometry, et cetera.

Euclid's axioms were half-intuitive, half-rigourous. As such, some of them can be replaced to form new and interesting non-Euclidean geometries.

Oh, and circle geometry is a subset of plane geometry, not a different geometry.

Also, elliptical geometry, hyperbolic geometry.