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RECTANGULAR CARTESIAN COORDINATES IN 2 DIMENSIONS
Introduction:
This topic is key in building the concept of location. The knowledge achieved from this topic can be used in locating places. In order to locate places you need a starting point (reference point).
A pair of values written in the form (xy) is called coordinates A point with given coordinates can be plotted on the x y plane
The x y plane is the same as the coordinate plane or the rectangular Cartesian plane
On the x y plane, the horizontal axis is called the x axis and the vertical axis is called the y axis.
The x axis meets the y axis at a point called the origin.
The coordinates of the origin are (0, 0)
On the x axis, values to the right of the origin are positive and those to the left are negative On the y axis, values above the origin are positive and those below are negative.
4.1 Identifying the x axis and y axis
Activity : Plotting Points
STEPS:
Find the value of x on the x axis. i.e Start from the origin (0,0) and move the required steps along the x axis.
Locate the value of y on the y axis. i.e Start from the origin (0,0) and move the required steps along the y axis.
The intersection of the x and y values is the point.
EXAMPLE
Plot the following points on a graph paper A(6,4), B(5,9), C(8,3), D(-4,4), E(-2,-8), F(2,-3), G(3,4),and H(4,-3).
SOLUTION
A(6,4). Start from the origin and first move 6 units to the right (because its positive) ,then 4 units upwards .The intersection is point A.
4.1 Exercise Set
1. (a) Plot the following points on a graph paper A(-4,2), B(-3,5), C(1,5), D(2,2), E(-5,-5), F(-3,-2),G(-1,-5), H(2,-2), I(8,2) , J(8,-4) and K(2,-4)
(b) Join points ABCDA,EFGE,HIJKH
(c) Name the figures formed in each case.
2. (a) Write down the points plotted on the graph paper below
(b) Join points ABCDA
(c) Name the figure formed in each case
4.2 Plotting Polygons (shapes)
A regular polygon is a polygon which is equiangular (all angles are of the same size) and equilateral (all sides have the same length).
EXAMPLE:
Join the points A(1,1) ,B(5,1) and C(3,4) to form a triangle
4.2 Exercise Set
2. Half of an Irregular octagon with one line of symmetry can be drawn by joining the points with coordinates: (0,-2), (-2, 0), (-2, 2), (0, 4) . Join the coordinates. You have drawn one half of the Irregular octagon. Complete the Irregular octagon. Write down the coordinates.
3. On the same axes, plot the points P(-3, 2), Q(-5, 0), R(-4,-3) S(-2,-3), T(-1,0) Join the points and name the formed figure PQRSTP.
4. On the same axes, plot the points P(3, 4), Q(5, 4), R(6, 2) and S(2, 2),Join the points and name the formed figure PQRS.
4.3 Use of Appropriate Scale for Given Data.
At times we encounter large values for x and y ,and for such cases we are required to use a convenient scale such that all our values can be able to fit on the graph paper.
EXAMPLE:
Plot the following points on the axes: A(5, 50), B(10,100), C(15,150), D(20,200), E(25,250) , F(30, 300), G(35,350).
you realise that on the horizontal axis(x- values) there are 5 units for each space and On the vertical axis (y- values)there are 50 units for each space
Horizontal scale : 1cm:5
Vertical axis :1cm :50
4.3 Exercise Set
1. For each part, draw a pair of axes with suitable scales and plot the points: (a) A(1, 15), B(4, 35), C(8, 45) (b) M(15, 100), N(35, 500), P(40, 700).
2. Plot the points X(2, 60), Y(4, 50), Z(0, 70), T(7, 60).
3. On the same axes, plot the following points A(4, 10 ), B(-2,-40), C(3, 0), D(0, 30), E(-3, 15) and F(0,-20).Use a scale of 1cm to represent 1 unit on the x- axis and 1cm to represent 5 units on the y- axis.
4. A quadrilateral has vertices A(-10, 0), B(-10, 25), C(15, 25) and D(25,-10). Plot the points of the quadrilateral and identify it. Use a scale of 2cm to represent 10 units on both axes.
Situation of Integration
A Senior One learner has reported in her class and has settled at her desk.
Support: The classroom is arranged in rows and columns. It is a big class with each learner having his/ her own desk.
Resources: Knowledge of horizontal and vertical lines i.e. rows and columns, coordinates Knowledge: counting numbers.
Task: The mathematics teacher has asked her to explain how she can access her seat, starting from the entrance of the class. Discuss whether there are other ways of reaching her seat.
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