5.8) Applications of coordinate geometry in the real world.

You might want to consider: a) the applications of coordinate geometry b) any challenging questions you will like to share?

Application [Introduction]

By Charles (2O2/30)

[Summary]

By Ng Jia Neng

By Lim Jerome

[Graphics]

One of the usage of coordinate geometry is on the vector computer graphics. This kind of graphics, unlike bitmap which uses dots or pixels to create graphics, uses mathematical equations to generate lines and colours. This kind of graphics is that unlike bitmap, the image will not get any blurrier no matter how you zoom it in. (By: Teoh Zhi Charles & Yeoh Li Yuan)

Comparison between vector computer graphics with another type of graphics (By Ng Jia Neng)

2D & 3D graphics [By Ng Jia Neng] Two-dimensional coordinate geometry, the use of algebraic equations to represent two-dimensional geometric shapes such as lines and polygons, is the basis for the design of computer graphic software. The computer code that generates the two-dimensional object on the screen is based on coordinate geometry formulas, such as the distance and midpoint formulas.
Three-dimensional coordinate geometry principles are also used in computer graphic programs. Many of the geometric formulas used in three-dimensional graphics computer programming are extensions of two-dimensional coordinate geometric formulas. For the rotation of a 3D geometric object in a computer graphic program, geometric point transformation procedures are used that rotate all the vertexes of the 3D object.

Geometry is used to automatically generate graphics.

[Maps]

One of the most important place where coordinate geometry is applied is in maps. Coordinate geometry in used in the data conversion process where each digital map is constructed from written descriptions, such as legal descriptions of land parcel boundaries. They often include details about line length and direction and point locations. (By Chuan Bin and Chen Yi)

Another important use for coordinate geometry is GPS. The GPS uses latitude and longitude to determind the position of a person of object. In the modern world, many of us cannot live without the all important GPS. (By Chuan Bin and Chen Yi)

For finding the distance between the places we are using coordinate geometry and in geography also it have many applications. In astrophysics to find the distance between the planets, coordinate geometry helps. (Taken from :http://www.tutorvista.com/math/uses-of-coordinate-geometry) [By Chuan Bin and Chen Yi]

Astronomers (and amateurs) use sky coordinates to locate objects of interest. Users of maps may use the coordinates provided on the edge to find a place of interest. (By Ng Jia Neng & Shawn Tan)

Coordinate geometry are used in manipulating images. The selected image is like a big coordinate plane with each colour information as each individual points. Thus when the colours of the pictures are being manipulated, the points are changed. (By Lim Jerome)

Coordinate geometry is used in manipulating images. (Lim Jerome)

Coordinate geometry are also used in a PDF file, the printed page is one big coordinate plane. Coordinate geometry is thus used to position elements on the page. PDF files that are produced contains text, images and line drawings, all of which are placed into position by using (x,y) coordinates, distances, slopes, and simple trigonometry. (By Lim Jerome)

Coordinate geometry is applied in scanners. (Lim Jerome)

[Scanners]

Coordinate geometry are also applied in scanners. Scanners make use of coordinate geometry to reproduce the exact image of the selected picture in the computer. It manipulates the points of each information in the original documents and reproduces them in soft copy. (By Lim Jerome and Jiang Hong Quan)

[Others]

In a sense, the mathematics underlying all fundamental science is based on coordinate geometry. That is, processes can be considered in terms of multi-variate functions, and all multivariate functions can be graphed (visually displayed) using coordinate geometry. (Taken from : http://in.answers.yahoo.com/question/index?qid=20101112033303AAgM8Ep) [By Chuan Bin and Chen Yi]

Thus coordinate geometry are widely used without our knowing. They are mostly commonly used in reproducing the original and also in IT forms. (By Jiang Hong Quan)

[Summary]

Challenging Questions

a)The distance between two points A(1, 3) and B(4, k) is 5. Find the possible values of k. (By Lim Jerome)

b)Convert the following expressions to a linear expression and state the Y(y-axis), X(x-axis), M(gradient) and C(y-intercept).(By Charles) i)y=2/x+x^2 ii)y=2x^2+3x

c)Define an algebraic expression to express a circle on a Cartesian plane. Hint: requires the Pythagoras's Theorem (By Charles)

5.8) Applications of coordinate geometry in the real world.You might want to consider:a) the applications of coordinate geometry

b) any challenging questions you will like to share?

Application[Introduction]

By Charles (2O2/30)

[Summary]

By Ng Jia Neng

By Lim Jerome

[Graphics]

Two-dimensional coordinate geometry, the use of algebraic equations to represent two-dimensional geometric shapes such as lines and polygons, is the basis for the design of computer graphic software. The computer code that generates the two-dimensional object on the screen is based on coordinate geometry formulas, such as the distance and midpoint formulas.

Three-dimensional coordinate geometry principles are also used in computer graphic programs. Many of the geometric formulas used in three-dimensional graphics computer programming are extensions of two-dimensional coordinate geometric formulas. For the rotation of a 3D geometric object in a computer graphic program, geometric point transformation procedures are used that rotate all the vertexes of the 3D object.

[Maps]

[Construction]

[PDF files & Images]

[Scanners]

[Others]

- In a sense, the mathematics underlying all fundamental science is based on coordinate geometry. That is, processes can be considered in terms of multi-variate functions, and all multivariate functions can be graphed (visually displayed) using coordinate geometry. (Taken from : http://in.answers.yahoo.com/question/index?qid=20101112033303AAgM8Ep) [By Chuan Bin and Chen Yi]
- Thus coordinate geometry are widely used without our knowing. They are mostly commonly used in reproducing the original and also in IT forms. (By Jiang Hong Quan)

[Summary]Challenging Questions

a)The distance between two points A(1, 3) and B(4, k) is 5. Find the possible values of k. (By Lim Jerome)

b)Convert the following expressions to a linear expression and state the

Y(y-axis),X(x-axis),M(gradient) andC(y-intercept).(By Charles)i)y=2/x+x^2

ii)y=2x^2+3x

c)Define an algebraic expression to express a circle on a Cartesian plane. Hint: requires the Pythagoras's Theorem (By Charles)

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