Lesson Notes By Weeks and Term - Junior Secondary School 2

SUBJECT: MATHEMATICS

CLASS:  JSS 2

DATE:

TERM: 2nd TERM

 
WEEK FIVE

TOPIC: THE CARTESIAN PLANE AND COORDINATES

CONTENT 

•  The position of points on aline 
• Cartesian plane/coordinates
• Plotting points

The position of points on a line 

The number line is a picture or graph of relative position of positive and negative numbers.

Worked Examples

1. Find the values of the following variables in the number line below:

      D        B                 C                A

                                             -4      -3      -2     -1     0     +1   +2     + 3     + 4 

Solution 

1. A is 3 units to right of zero = A ( 3)
2.   B is 1 unit to left of zero = B (-1)

iii.  C is 1 ½ units to the right of zero = 1 ½ 

1. D is 2 units to the left of zero = ( -2)
2. Draw a number line from -5 to 5 in the number line mark.
3. 2     B. (-4)        C. ( -2 ½ )   and D. ( 1)

Solution

      D        B                 C                A

    -4      -3      -2     -1     0     +1   +2     + 3     + 4 

Evaluation

1. Give the position of 1A   ii. B  iii C   iv. D   v. E in the number line below:
2. Find the values of the following variables in the number line below:

      D        B                 C                A

    -4      -3      -2     -1     0   +1   +2     + 3     + 4 

3. Draw a line from -8 to 5 and indicate the following points x ( -2) , y(3) W(4)  M (5) x (-6) and T(-8)

READING ASSIGNMENT 

New General Mathematics UBE Edition, Chapter 12, Nos 1- 2pgs102-107

Essential Mathematics by A. JS. Oluwasanmi Chapter15 pgs 152 -155

Cartesian Plane/Coordinate 

Cartesian graphs give a picture of the relative position of point on a plane.  The Cartesian plane is a plane surface with two axes drawn on it.  The axes  are at right angle to each other . they are the horizontal ( x –axis) and the vertical (y-axis) crossing at the origin (the zero point for both axes).

    Y – axis(positive )

x-axis (negative)        x- axis(positive)

y axis (negative)

COORDINATES

Every points on the Cartesian plane has a unique ordered pair of coordinates in the form ( a,b) where a is x – coordinates (distance of the point along the x – axis) and b is the y-coordinates ( the distance of the point along the y-axis).

Worked Examples

1. Write down the coordinates of the point A,B,C,D,E and F in the figure below:

    C    6-    A

                                                                                               5-   

                                                                                               4-

                                                                                               3-

                                                                                               2-

                                                                                               1-

              -5 -4  -3  -2  -1        1   2   3   4    5 

    -1

    -2

    -3

    D    -4    B

2.     Write down the coordinates of the vertices of triangle ABC and parrellogram PQRS in the figure below

Solution 

1. The coordinates of the points are 
2.   A (3, 5)
3. B 9 2, -4)

iii. C ( 2, -3)

1. D (-3,-4)
2. E ( 4,0)
3. F ( 1, -1)
4. The vertices of triangle ABC are A. ( -2,3) B. ( 2,1) C ( 0, -1)

The vertices of parallelogram PQRS are P ( 1,2)    Q ( 1,2)    R(-2,-2)    S (-3,0)

EVALUATION 

1. What are the coordinates of the points A B C, D, E, F, G, H  in the figure below

2. In the figure below name the points which have the following coordinates
3. (9,5)   b. (5, - 8 )     c. (-15,10  )   d    (-5, 8  )  e  (12, 0 )

GENERAL EVALUATION 

Show the position of the following points on the graph sheet . using 1cm to 1 unit on both axes.

1. P (2, 4)   Q (-3, -4)  R   (2, -4)  S   (-12,9) T (8, -15 ) 

READING ASSIGNMENT 

New General Mathematics UBE Edition, Chapter 12, Nos 1- 2pgs105-107

Essential Mathematics by A. JS. Oluwasanmi Chapter15 pgs 237-239

Plotting Point

Plotting points means to draw its positions on Cartesian plane. The easiest way to plot a graph is as follows :

Start at the origin 

1. move along the x axis by amount and in a direction given by the x-coordinates of the point .

iii. move up or down parallel to the y-axis by an amount in a direction given by the y- coordinates.

Worked Example

1. Plot the point ( -1,2) and ( 2,6-1.8) on a Cartesian plane . 

1. The vertices of quadrilateral PQRS have coordinates P (-3,18) Q ( 15,14)  R (11,-4) and S ( -7,0) A and B are the 

          points A(-3,-7) and B ( 3,0).

1. using a scale 2cm, represent 10 units on both axes  plot points P.Q, R .S.A and B.
2. join the vertices of quadrilateral PQRS. What kind of quadrilateral is it?
3. Find the coordinates of the points where diagonal of PQRS cross. 

Solution

a

1. PQRS is a square
2. the diagonals of PQRS  cross at x(4,7)
3. B. A  and Q lie on the same straight line

REVISION QUESTION 

1. Draw the origin O, near the middle of a sheet of graph paper use a scale of 2cm represent 5 units on both sides. Plot the following points. Join each points to the next in order they are given start (-10,-5 ) (-5,10)  (0,15) (5,17) (3,14)  (3,12)  (15,6)   (14,3)  (11,3),1  (13,2)  (5,3)  (6,-6) >

What pictures does your graph shows.

WEEKEND ASSIGNMENT 

1. Use the diagram below to answer questions 1-3

            A     C    B    D    E

    -4      -3     -2     -1   0   1     2      3

2. The value of a is  A. 3 ½         B. -4        C. 3        D. 1  ½
3. The value of D is  A. -4     B. 1 ½        C. -3 ½        D. 3
4. The value of C is A. -4     B. 1 ½        C. 3 ½        D. 3
5. if the value of a point in the x axes are 2 and -4 respectively, it can be written in a 
6. ( 2,-4)     B. ( -4,2)    C. ( y ,2)        D. ( x, 2)

5. Point A in the diagram is A. (-5, 5)     B.(5,5)          C(-5,-5)      D.  (0,5) 

THEORY

1. Draw the graph of the following coordinates and join all the points.

    T(-2,1) U (-3,1)  V(0,4)  W(3,1)  X (2,1)  Y(2,-1) Z(-2,-1)

2. Draw the origin  () near the middle of a sheet of graph paper use scale of 2cm represents 1 unit on both 

    axes. Plot the following point, and then join each point to the next in alphabetical order.

    A(0,1) B(1,2)C (1,1) D(2,1) E(1,0)F (2,-1)G (1,-1)H (1,-2) I(0,-1) J(-1,-2) K(-1,-1)L (-2,-1) M(-1,01) N(-2,1)

    P (-1,1) Q(-1,2) finally join Q to A.