雙語教學主題(國中七年級教材):介紹座標平面 Topic: introducing coordinate plane
下面是這個單元需要用到的單字
Here are some of the words we will use in the class
number line horizontal line vertical line origin 原點 x axis y axis
unit quadrant 象限 plot ordered pair 數對 perpendicular intersect
coordinate plane 座標平面 x- coordinate y- coordinate dimension 維度
Before we introduce the coordinate plane, let’s review “number line” we learned
A number line is a horizontal straight line with numbers placed at
equal intervals or segments along its length. The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.
A unit is the distance between every 2 consecutive integers.
-9-8-7 -6-5-4-3-2-1O 1 2 3 4 5 6 7 8 9
Now we place a number line vertically on the plane as it shows.
These two number lines are perpendicular to each other, and intersect at their zeroes
The horizontal line is called the x-axis, and the vertical line is called the y-axis We can see the positive numbers are above zero along the y-axis, and the negative numbers are below zero for the verticle axis.
A number line is one dimensional, all the points we plot will stay on the line, but here we have a two dimensional plane, we now can show all the locations of the points on the coordinate plane using the corresponding x- and y- values
We use ordered pairs like (x,y) (we say parentheses x comma y), to represent where the points are along x or y- axis on the plane.
Remember x- value comes first and y- value comes second, the order matters are always the same
The first number x is called the x-coordinate and the second number y is the y- coordinate
y
x 1
2 3 4 5 6 7 8 9
-5 -4 -3 -2 -1
-6 -7 -8 -9
-9-8-7 -6-5-4-3-2-1 1 2 3 4 5 6 7 8 9 O
same order
y coordinate x coordinate
(x,y)
That’s why it’s called the coordinate plane.
For instance, the intersection of x- and y- axis is (0,0) which means the intersection point is located on x=0 and y=0
This point is called the origin.
origin (0,0)
y
x 1
2 3 4 5 6 7 8 9
-5 -4 -3 -2 -1
-6 -7 -8 -9
-9-8-7 -6-5-4-3-2-1 1 2 3 4 5 6 7 8 9 O
Another example: Find the location of the point (5,2) on the coordinate plane The first number positive 5 represents the position on x axis, staring from the origin, we move 5 units in the positive x direction and the second number positive 2 represents the position on y axis, starting from the origin, we move 2 units in the positive y direction
x=5 and y=2
5,2
5 2
5,2
y
x 1
2 3 4 5 6 7 8 9
-5 -4 -3 -2 -1
-6 -7 -8 -9
-9-8-7 -6-5-4-3-2-1 1 2 3 4 5 6 7 8 9 O
Let’s see some more examples
Please plot the following points on the coordinate plane (-6,5),(-2,-3),(4,-5)
For the point (-6,5), we know x=-6 and y=5
Since x is negative 6, we move 6 units in the negative x direction from the origin, then move 5 units up in the positive y direction
x=-6 and y=5
-6,5
5 6
-6,5
5,2
y
x 1
2 3 4 5 6 7 8 9
-5 -4 -3 -2 -1
-6 -7 -8 -9
-9-8-7 -6-5-4-3-2-1 1 2 3 4 5 6 7 8 9 O
When we finish plotting the points above, we get the location of these 4 points on the coordinate plane
These points locate in different regions of the coordinate plane We name these regions quadrants
The upper right region is quadrant one The value of x- and y- coordinates are both Positive
The upper left region is quadrant two
-2,-3
4,-5
-6,5
5,2
y
x 1
2 3 4 5 6 7 8 9
-5 -4 -3 -2 -1
-6 -7 -8 -9
-9-8-7 -6-5-4-3-2-1 1 2 3 4 5 6 7 8 9 O
The value of x- coordinate is negative and y- coordinate is positive The lower left region is quadrant three
The value of x and y- coordinates are both
Negative and the lower right region is quadrant four
The value of x- coordinate is positive and y- coordinate is negative
In counterclockwise direction, we get four quadrants on the coordinate plane
+,-
-,-
-,+ +,+
quadrant four
quadrant two quadrant one
quadrant three
O
1 2 3 4 5
-5 -4 -3-2 -1 6
-7-6 7 8
-8 9
-9
-9 -8 -7 -6 -1 -2 -3 -4 -5 9 8 7 6 5 4 3 2 1
x y
Normally Roman Numerals are used to label these quadrants
Beware, x and y axes don’t belong to any of the quadrants We say
The coordinate plane consists of four quadrants and 2 axes
Now let’s do some practice here
IV III
II I
O
1 2 3 4 5
-5 -4 -3-2 -1 6
-6
-7 7 8
-8 9
-9
-9 -8 -7 -6 -1 -2 -3 -4 -5 9 8 7 6 5 4 3 2 1
x y
This is a map of a community
1. Please find out all the x, y- coordinates for the location of the school, the baseketball court, the post office, the park, the library and the
convenience store
Ans:
School: library: park:
post office: basketball court:
convenience store:
2. What quadrant is the school in?
3. Are the convenience store and the park in the
We take the location of the school as an example
Starting from the origin, we move 2 units left to negative 2 on the x axis, then move up 4 units to the school, so the x, y- coordinates of the school is (-2,4)
We say it’s negative 2 comma 4
Ans:
School:
(-2,4) library: (6,4) park: (2,-8) post office: (-7,-8)
basketball court:(2,1)_ convenience store: _(6,-5)
2. What quadrant is the school in?
The schpp; is in the second quadrant
3. Are the convenience store and the park in the second quadrant?
(yes or no? If no, please write down the correct answer)
No, they are in the fourth quadrant
park
library
convenience store basketball court school
post office
y
x 1
2 3 4 5 6 7 8 9
-5 -4 -3 -2 -1
-6 -7 -8 -9
-9-8-7 -6-5-4-3-2-1 1 2 3 4 5 6 7 8 9 O
second quadrant?
(yes or no? If no, please write down the correct answer)
製作者: 北市金華國中 郝曉青
