Subject: Trigonometry

# Coordinate Geometry

## Trigonometry.CoordinateGeometry History

September 03, 2010 by math2 -
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'''1) 8.544'''\\
to:
'''1) {$\sqrt{{(9 - 1)^2} + {(4 - 7)^2}}$} = 8.544'''\\
September 03, 2010 by math2 -
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# Between (12, -12) and (-4, -7)
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'''1) (4, 11)'''\\
to:
'''1) {$\left({{2+6\over2} , {17+5\over2}}\right)$} = (4, 11)'''\\
'''3) (4, -9.5)'''
September 03, 2010 by math2 -
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September 03, 2010 by math2 -
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%center%%width=265px%Attach:taxi.jpg
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(:cellnr bgcolor=#d4d7ba colspan=14 align=center:) '+'''The Breakdown'''+'
(:cellnr:)
*[[#distance | The distance between two points]]
*[[#midpoint | The midpoint of a line segment]]
(:tableend:)
[[#distance]]
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Or this same equation can be expanded into three dimensions and used for space travel (you don't think it's important for astronauts to know how far they're going?).
to:
Or this same equation can be expanded into three dimensions and used for space travel (don't you think it's important for astronauts to know how far they're going?).
[[#midpoint]]
!!Midpoint of a line segment:
Finding the midpoint between two points is normally ever used to make word problems more difficult. But since it is used, you will have to know how it's done (but don't worry, this will be mindblowingly easy). You could figure out the length and slope of the line, convert it to a distance along the x-axis, and then figure out the y coordinate through the 'y=mx+b' equation.

Or take the short short short-cut, where given (x'_1_', y'_1_') and (x'_2_', y'_2_') the midpoint of the segment is:
{$$\left({{x_1+x_2\over2} , {y_1+y_2\over2}}\right)$$}

!!! Examples:

Find the following Distances:

# Between (2,17) and (6,5)
# Between (-5,-7) and (9,-4)

(:toggle id=box1 show='Show Answers' init=hide button=1:)
>>id=box1 border='1px solid #999' padding=5px bgcolor=#edf<<
'''1) (4, 11)'''\\
'''2) (2, -5.5)'''\\
>><<
September 02, 2010 by math2 -
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%center%%width=265px%Attach:taxi.jpg
September 02, 2010 by math2 -
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%width=265px%Attach:taxi.jpg
September 02, 2010 by math2 -
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!!! Distance between two points:
to:
!! Distance between two points:
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!!!! Examples:
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!!! Examples:
September 02, 2010 by math2 -

!!! Distance between two points:

Finding the distance between two points boils down to a simple formula. To understand the scope of this equation, understand that the entire world is on a coordinate system (longitude and latitude) and your house may be one point on that large coordinate system, and your friend Matt's may be another. If you wanted to find the distance between your house and Matt's house you could use this equation.

Or this same equation can be expanded into three dimensions and used for space travel (you don't think it's important for astronauts to know how far they're going?).

Given two points, (x'_1_', y'_1_') and (x'_2_', y'_2_'), the distance between these points can be found as:
{$$\sqrt{{(x_2 - x_1)^2} + {(y_2 - y_1)^2}}$$}

And for all you future physicists, for three dimensions you could use: (x'_1_', y'_1_', z'_1_') and (x'_2_', y'_2_', z'_2_'), & the distance between these points can be found as:
{$$\sqrt{{(x_2 - x_1)^2} + {(y_2 - y_1)^2} + {(z_2 - z_1)^2}}$$}

!!!! Examples:

Find the following Distances:

# Between (1,7) and (9,4)
# Between (-5,7) and (9,4)
# '''Hard:''' Between (-2,7,12) and (5,-9,14)

(:toggle id=box1 show='Show Answers' init=hide button=1:)
>>id=box1 border='1px solid #999' padding=5px bgcolor=#edf<<
'''1) 8.544'''\\
'''2) 14.3178'''\\
'''3) 16.4012'''
>><<

August 19, 2010 by math2 -
%rframe% %width=265px%Attach:taxi.jpg
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%cframe width=275px border='2px solid black' padding=5px% %width=265px%Attach:taxi.jpg

%center% %width=300px% Attach:GraphPaper.gif

As you can see a standard graph with an x and y-axis along with numbers along the x-axis.
August 19, 2010 by math2 -
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As a taxi cab driver we're going to stick to straight lines at first.. Then we'll start getting creative. To recap a little [[Geometry\Geometry]] here is a coordinate plane:
to:
As a taxi cab driver we're going to stick to straight lines at first.. Then we'll start getting creative. To recap a little [[Geometry/Geometry]] here is a coordinate plane:
August 19, 2010 by math2 -
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As a taxi cab driver we're going to stick to straight lines at first.. Then we'll start getting creative. Here is a coordinate plane:
to:
As a taxi cab driver we're going to stick to straight lines at first.. Then we'll start getting creative. To recap a little [[Geometry\Geometry]] here is a coordinate plane:
August 19, 2010 by math2 -
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%cframe width=275px border='2px solid black' padding=5px% %width=265px%Attach:taxi.jpg\\
to:
%cframe width=275px border='2px solid black' padding=5px% %width=265px%Attach:taxi.jpg

As a taxi cab driver we're going to stick to straight lines at first.. Then we'll start getting creative. Here is a coordinate plane:
July 22, 2010 by misslee -
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The easiest way to remember what Coordinate Geometry is to think of yourself as a taxicab driver. You can only take streets by the block; you can't quite cut through buildings, right? Well, to start with, that's how we'll envision ourselves to better understand coordinate geometry.
to:
The easiest way to remember the general meaning of Coordinate Geometry is to think of yourself as a taxicab driver. You can only take streets by the block; you can't quite cut through buildings, right? Well, to start with, that's how we'll envision ourselves to better understand coordinate geometry.
July 22, 2010 by misslee -
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The easiest way to remember what Coordinate Geometry is to think of ourself as a taxicab driver. You can only take streets by the block; you can't quite cut through buildings, right? Well, to start with, that's how we'll envision ourselves to better understand coordinate geometry.
to:
The easiest way to remember what Coordinate Geometry is to think of yourself as a taxicab driver. You can only take streets by the block; you can't quite cut through buildings, right? Well, to start with, that's how we'll envision ourselves to better understand coordinate geometry.
July 22, 2010 by misslee -
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Coordinate Geometry has a few synonyms: cartesian geometry (probably one of the more well-known identifiers), analytic geometry, or analytical geometry. So if you're teacher is calling it something else in class, no worries.
to:
Coordinate Geometry has a few synonyms: cartesian geometry (probably one of the more well-known identifiers), analytic geometry, or analytical geometry. So if your teacher is calling it one of these other names in class, no worries.
July 22, 2010 by misslee -
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The easiest way to remember what Coordinate Geometry is to think of ourself as a taxicab driver. You can only take streets by the block; you can't quite cut through buildings, right?
to:
The easiest way to remember what Coordinate Geometry is to think of ourself as a taxicab driver. You can only take streets by the block; you can't quite cut through buildings, right? Well, to start with, that's how we'll envision ourselves to better understand coordinate geometry.

%cframe width=275px border='2px solid black' padding=5px% %width=265px%Attach:taxi.jpg\\
July 22, 2010 by misslee -