## Saturday, 20 April 2013

### Coordinate Geometry - Cartesian Plane (review lower secondary work)

By Mr Johari

Watch the following video and answer the questions that follow:

.1 What is the significant of Cartesian plane?
.2 Give an example of an ordered pairs and explain all the terms used.
.3 What is the significant of the 4 quadrants in the Cartesian plane?
.4 Give an example of the application of Cartesian plane. (some examples are shown below)

1. 1. A cartesian plane is used to accurately pinpoint a location on a 2D plane by using a vertical line and a horizontal line, known commonly as the y-axis and the x-axis. The information is then represented in an ordered pair.

2. An ordered pair is used to show the location of a certain point. The pair is shown in a format of (x, y), where x is the value of the point on the x-axis, the horizontal plane, and the y value of the point on the y-axis, the vertical plane.

The point can also be known as where the two lines, x and y, meet.

For instance, the point z rests on (2,2). This shows that x = 2 and y= 2. By draw two lines, y = 2 and x = 2, we can find the intersection of these two lines, which is shown in the format (x, y).

3. The 4 quadrants in the cartesian plane can be used quickly to find the location of a point by looking at the ordered pair. For instance, point z is on the coordinates (2, -2). By looking at the x and y value, we can quickly determine the location of point z, which is in Quadrant 4. Thus, the 4 quadrants in the cartesian plane divides the positive and negative values of x and y and allows one to find the location of a point quickly.

4.A cartesian plane can be used to pinpoint a location on a 2D plane accurately. For instance, a map would have a x and y-axis, which can be used quickly to determine a certain location or building. Thus, instead of looking through an entire map, a coordinate would be given to someone to read so that the location can be easily pointed out.

2. 1. The cartesian plane is used to plot the exact locations on a certain 2D plane using lines to and their intersections to form 'coordinates'.

2. An ordered pair is a pair of coordinates within a bracket, usually the value of the horizontal line and then the vertical line separated by a comma. In math, we use the (x, y) as the horizontal axis is the x axis while the vertical axis is the y axis.

3. The four quadrants determine values of the desired ordered pair. For example, if we know the x-value is a negative, we can go to quadrant 2 or 3, and if we know the y-value is positive, we can confirm that it is in quadrant 2.

4. An example is in maps, where we have northings and eastings. In this case, lines that pile upwards (easting) are the first coordinate, and lines that pile horizontally (northings) are the second coordinate.
In this case giving someone the value (222, 890) will allow them to find the desired location on a map.

3. 1. What is the significant of Cartesian plane?
It is very important in making maps and determining the exact value of something on a @D plane.

2. Give an example of an ordered pairs and explain all the terms used.
An example would be (1,1). Ordered pairs are values of x and y between a bracket, showing the position of a dot on the coordinate system. It is in the general form (x,y).

3. What is the significant of the 4 quadrants in the Cartesian plane?
The quadrants in the cartesian plane will determine what is the general value of x and y, for example if something is in the first quadrant, the value of x and y would always be positive.

4. Give an example of the application of Cartesian plane.
The cartesian plane can be used making maps and finding the longitude and latitude. Also, the cartesian plane can be used in solving equations graphically.

4. 1. A cartesian plan a rectangular coordinate system with x-axis and y-axis that associates each point in the plane with a pair of numbers which is otherwise called an ordered pair.

2. An ordered pair would be (x,y) . x being the x- co ordinate which is the vertical line of x while y being the y-co ordinate which is the horizontal line of y. The intercept of the two lines would then "creates" the ordered pair.

3. The 4 quadrants is a way to divide between the negative/positive signs of the ordered pair (x,y).
First Quadrant - (+ve x , +ve y)
Second Quadrant - (+ve x , -ve y)
Third Quadrant - (-ve x, -ve y)
Fourth Quadrant - (-ve x, +ve y)
This is organised in clockwise rotation.

4. An example would be a map where its positon in marked by the latitude and longitude which is similar to (x,y)

5. 1.determine the position of point and show them in coordinate.
2.(2,7) 2-x coordinate 7-y coordinate
3.By the observing the negative and positive sign before the numbers and relate it to the quadrants characteristic, we can find the location of the point quickly.
4. Cartesian plane can be applied in finding the location of some symbols on the map.

6. 1. Cartesian co-ordinates represented on a cartesian plane.
2. It is in the format of (x,y) and is represented by it's intersection on x axis when we draw a line x=x and y axis when we draw a line y=y. For example, the ordered pari (2,3). When we draw a line x=2, it's intersection at the x axis is 2. When we draw a line y=3, it's intersection at the y axis is 3.
3. It tells us whether each x and y value is positive or negative, depending on which quadrant it is in out of the four quadrants.
4. A cartesian plane can show accurately the co-ordinates of a specific place in a map.

7. 1. A cartesian points has many grids that divide it into specific areas . An ordered pair (Coordinate) is able to give us the exact location of this point which we can then use to plot graphs . There is a vertical line going the full length of the paper , this is the y-axis which is used to determine how high from the origin a point is . There is a horizontal line also going through the width of the paper , this is known as the x-axis which tells us how far away from the origin a point is .

2. It is represented by (x,y) . X is how far away the point is from the x-axis , which is the x value of the point . Y represents how high the point is , or the y - value of the point . All of this help to determine where the point will be located at .If we plot the x value graph and the y value graph , there will be an intersection somewhere on the cartesian plane . This is where the ordered pair will be at .

3. There are 4 quadrants that divide the cartesian plane . In the upper right quadrant , both the x and y values will be positive , at the upper left quadrant , the x value is negative but the y value is positive . In the bottom left quadrant , the x and y values are negative . Lastly , in the bottom right quadrant , the x value is positive and the y value is negative . The quadrants can be used to help plotting of the graph , by looking at whether the x and y values are positive or negative , we can determine which quadrant it is in .

4. A map . A map is further divided into grids , by giving the x and y values , we are able to find a place of interest etc.

8. 1. A Cartesian plane is an unbounded two-dimensional shape. It includes an x and y axis. We can pinpoint a certain location using a horizontal and vertical line.
2. An ordered pair is represent in this format. (x,y) With x being the x coordinate and y being the y coordinate of the specific point.
3. The 4 quadrants are able to divide the plane into 4 distinct quadrants. One with the x and y being positive, one with them both negative, the x is positive while the y is negative and the y is positive while the x is negative. This allows us to locate the point much more easily with reference to the center.
4. Mapping, architecture, engineering.

9. 1. The cartesian plane can locate a location on a 2D plane by using x and y coordinates, or a vertical and a horizontal line which is also known as the x and y axis.
2. An ordered pair is a pair of x and y coordinates in a bracket, (x,y), deriving their values by drawing a vertical and horizontal line that cuts the x and y axis. Thus getting the x and y value.
3. The quadrants allow us to identify if the value is negative of positive and also the values of the coordinates of the ordered pair.
4. It allows us to find a point on a map quickly by looking through the x-axis and y-axis to find the desired values of x and y, followed by looking for an intersection of the lines.

10. 1. Used to identify a point on a 2D plane. Points on that 2D plane are represented by its value on the y and x axis. The 2 values are then represented as an ordered pair. This allows any point on the 2D plane to be represented. This can be used to find locations on a map, or to look at relationships between numbers

2. Ordered pairs are written in the form of (x, y) where x and y are the values on the x and y axis respectively. For example, a point that is at 3 on the x axis and 5 on the y axis will be written as (3, 5). The x-axis is a horizontal line that that runs through the point where the y axis is 0 while the y axis is a vertical line that runs through the point where the x axis is 0, so the x and y axis intercept each other. The point where the x and y axis intercept each other is known as the origin.

3. The 4 quadrants are numbered from 1 to 4 in a anti clockwise direction starting from the top right quadrant. They allow us to find points on the cartesian plane easily. This is because points in quadrant 1 have a positive x and y value. Points have a positive y and negative x value for quadrant 2, negative x and y value for quadrant 3, and a positive x and negative y value for quadrant 4. This helps us to identify the position of an ordered pair on the cartesian plane easily

4. The cartesian plane is used in maps to be able to identify the exact position of the place that we want to go to. It can also be used to show relationships in the form of graphs as when the points are plotted on the cartesian plane , we will be able to clearly observe a trend.

11. 1. A cartesian plane allows points to be accurate placed on the 2D grid, using the x and y axis.

2. And example of an ordered pair is (3,2). This means that the point is on point 3 on the X-axis, and on the point 2 on the Y-axis. It can be used to pinpoint coordinates on the cartesian plane.

3. The 4 quadrants can be used to quickly have a general idea where the coordinates are. This is so as Quadrant 1 consists of all positive x and y values, Quadrant 2 consists of negative x and positive y values, Quadrant 3 consists of negative x and y values, and Quadrant 4 consist of positive x and negative y values. The x and y points can then be identified closely using the ordered pair (x,y).

4. In Geography, the Cartesian Plane is stretched across the globe and used for making maps. Latitude and Longitude coordinates are recorded as ordered pairs on the cartesian planes.

12. 1) A cartesian plane is significant as it can be used to find locations in reference to their position on a vertical and horizontal line commonly known as the y and x axis respectively.

2) An ordered pair is they way you would present the position on the cartesian plane. (x value, y value)

3) The 4 quadrants each have their own kind of ordered pair. 1st quadrant x=+ y=+ 2nd quadrant x=- y=+ 3rd quadrant x=- y=- 4th quadrant x=+ y=-

4) Cartesian plane can be seen used in the a map as it has both horizontal and vertical values and as such effectively locate a particular location with accuracy.

13. 1. A cartesian plane is used to locate a point on a plane with the use of a horizontal line, known as the x-axis, and a vertical line, known as the y-axis.

2. An ordered pair can show the location of a point on a cartesian plane. This ordered pair is written as (x,y), where x is the value on the x-axis and y is the value on the y-axis.

An example is a map. In Geography, when we do map reading, we make use of ordered pairs to identify and locate a particular location. The eastings in the x-axis and the northings is the y-axis. Using this, we are able to find the location of that point.

3. it represents different x and y values. It divides the cartesian plane into (+,+), (-,+), (-,-) and (+,-). This helps us identify whether the ordered pair is a negative or positive one.

4. A cartesian plane can be used in a map. When travelling, we make use of maps to help us find our way. This map is a cartesian plane that has a x-axis and a y-axis. The map can help us find the location we want to travel to.

14. 1. A Cartesian plane is used to accurately locate a location on a 2D surface.

2. An example of an ordered pair would be (2, 5). The first number, 2, shows that horizontal position of the point from the origin and the second number, 5, shows that vertical position of the point from the origin.
Therefore the ordered pair (2, 5) shows that the point is 2 units to the right of the origin and 5 units above the origin.

3. The 4 quadrants are number I to IV starting from the top right quadrant, moving clockwise.
The 4 quadrants determine the signs (positive or negative) of the two coordinates. I = (+,+), II = (-,=), III = (-.-) and IV = (+,-)

4. An application of the Cartesian plane would be the a mapping of earth. The earth has its longitudes and latitudes which acts like the x and y axis of a cartesian plane. Each location on the map of earth had its own combination of longitude and latitude.

15. .1 A plane in which all points are defined using 2 lines which is also known as the x and y axis. The plane is divided into 4 quadrants. (++) (+-) (-+) (--)
.2 Each point of the coordinate system is identified by by ordered pairs which indicates where the point is along the x and y axis.

.3 It indicates where there the x coordinates or y coordinates are positive or negative.

.4 Cartesian plane could be used for navigation and orientation.

16. 1. What is the significance of Cartesian plane
It is used to determine location of points on a 2D plane in order to find directions, plot graphs or finding points of intersection

2. Give an example of an ordered pairs and explain all the terms used.
(2,3) is an example of ordered pairs where 2 is the x coordinate and 3 is the y coordinate. The ordered pair consist of 2 values within brackets separated by a comma where the first value is the x and the second value is the y value

3. What is the significant of the 4 quadrants in the Cartesian plane?
The quadrants of the cartesian plane determine the value of the x and y, for example when a point is in the 3rd quadrant both x and y are negative

4. Give an example of the application of Cartesian plane.
It can be used in the making of maps and solving equations graphically.

17. 1. A cartesian plane is a plane which has a vertical line( Y-axis) and a horizontal line(X-axis). These two lines have coordinates and they meet each other at origin-(0,0).

2. For instance, an ordered pair (1,2) indicates the place where line X=1 and line Y=2 meet each other.1 is the coordinate on x-axis and 2 is the coordinate on Y-axis

3. The ordered pairs in Quadrant 1 have positive X values and positive y values;
In Quadrant 2, the pairs have negative Y values and positive X values;
In Quadrant 3, the pairs have both negative X and Y values;
In Quadrant 4, the pairs have positive X ales and negative Y values.
We easily tell where the point is by looking at the X and Y values.

4. An example of the application of Cartesian plane is map.

18. 1. The cartesian plane is significant as it can help determine the exact location or value of a particular point on a 2D plane.

2. An example of an ordered pair is (1,2). It is usually represented in the form of (x,y). This shows the position of the point or dot on the 2D plane.

3. The 4 quadrants in the Cartesian plane determines whether the values of x and y will be negative or positive.

4. An example of an application of the Cartesian plane would be a map. There are different lines on the map to help pinpoint different locations to help find the desired location of something.

19. 1. What is the significance of Cartesian plane It is used to determine location of points on a 2D plane.

2. Give an example of an ordered pairs and explain all the terms used. (2,5) is an example of ordered pairs where 2 is the x coordinate and 5 is the y coordinate. The ordered pair consist of 2 values within brackets , they are separated by a comma.

3. What is the significant of the 4 quadrants in the Cartesian plane? The quadrants can determine the coordinates of points are negative or positive.

4. Give an example of the application of Cartesian plane. It can be used in the making of maps.