WildTrig12: Cartesian coordinates and geometry

Cartesian coordinates allow us to talk precisely about points and lines, parallel and perpendicular, and quadrance and spread---the two main concepts from rational trigonometry.

Category:

Science & Technology

Tags:

• Cartesian
• coordinates
• points
• lines
• parallel
• perpendicular
• quadrance
• spread
• Descartes
• Fermat

[HoneyDogW]

Dumb Question: Great explanations! But I didn't quite follow how you go from a vector of (1,-3) to the equation 3x+y=?

On the next line you explain the formula

vector=(alpha,beta):-betaX+alp­haY=?

However, if I redefine the vector as (-1,3), which is still the same line, I now get -3x-y=-7

Are these equivalent equations? Its been a long time since I've used anything but +,-,*,/ and I'm trying to wrap my head around this again :) Thanks.

[njwildberger]

Hi. The direction vector doesn't completely determine the line. So if you used (-1,3) as the vector, which is fine, you would get an equation for the line: -3x-y=c for some constant c. To determine c, plug in a point you know on the line.

For example the line 3x+y=4 is the same as the line -3x-y=-4. Hope this helps

[GGinFra]

Omg! I've just realized that Dr.Wildberger and Mr.Connery are the same person ! ^^

[smilerLFC]

@Mephistophilus Why make things complicated... Is it that hard to grind food??

[TheNubletLord]

Is that a drum stick?

[misyanto86]

ok..I love it..

[Mephistophilus]

It's used for geo statistical analysis to warn you of soil toxicity, population density, traffic congestion, etc. It's used in resolving heat transfer problems. Game programming. Movie effects. Keeping planes from slamming into each other. It occurs grinding food waste and carrying water out of your home. Check out Spira Mirabilis. Trig is everywhere in your daily life.

[TiN0350]

what the shit do we actually use this for in daily life...