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Coordinates the modern way!

November23

So, you are sitting in a math class, wondering why you are doing Coordinate Geometry? descartes

You know the feeling – using (x,y) to show the place of a point on a Cartesian Plane. The Cartesian Plane was named after the French mathematician, Rene Descartes (right). He was a really bright Math guy as well as a philosopher, although that long hair might have not gone down too well in some classrooms today! Anyway, back to your class…

The teacher tells you that the coordinates go in alphabetical order – that is, “x before y in the alphabet…so x before y in a coordinate.” You kind of get that but are still wondering when you will ever come across a coordinate system in real life. After all, the car and your smartphone have a built in GPS mapping system, which is really easy to use.

Well, here is a coordinate system in action and it is used for detailed property information in New Zealand’s largest city – Auckland. In the diagram below you will see the (x,y) system being used in the upper right corner. Click on the image and it will take you to the live GIS viewer. GIS means “Geographic Information System“, which is a very sophisticated layer system of land information. Move your cursor around and you will notice the (x,y) coordinates change as they focus on a specific part of the map. If you need an address to get more detail, try “1 Nile Road” for example (case sensitive).
GISViewer

 

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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