Topic 4:
RECTANGULAR CARTESIAN
COORDINATES IN 2 DIMENSIONS
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Key words: coordinates, axes, plot, scale
By the end of this topic, you should be able to:
i) identify the y-axis and x-axis.
ii) draw and label the Cartesian plane.
iii) read and plot points on the Cartesian plane.
iv) choose and use appropriate scale for a given data set.
v) identify places on a map using coordinates (apply coordinates
in real-life situations).
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).
Sub-topic 4.1: Identify the X-axis and Y-axis
Activity 4.1: Plotting Points
Now, plot the following points on a graph, (6,4), (5,9), (11,3), (5,6) and (3, 4).
The x number comes first then the y number: (X, Y). These numbers are called coordinates.
Exercise
1. Use a graph paper to:
a) Join the points with coordinates (0, 3), (5,6), and (5,0) to draw a triangle.
b) On the same diagram join the points with coordinates (2, 0), (2, 6) and (7, 3) to draw a second triangle.
c) Describe the shape you have now drawn.
2. On the same graph paper join these points in order.
a) (4, 6), (5, 7), (6, 6), (4, 6).
b) (5, 8), (4, 8), (4, 7), (5, 8), (6, 8), (6,7), (5, 8).
c) (4, 5), (5, 4), (6, 5), (5, 3), (4, 5).
d) (5, 2), (3, 4), (3, 5), (2, 5), (2, 8), (3, 8), (3, 9), (7, 9), (7, 8), (8, 8), (8,
5), (7, 5), (7, 4), (5, 2).
We can also use negative numbers in coordinates. We can bring in coordinate axes with positive and negative numbers.
Exercise
1. (a) Draw a set of axes and mark the points with coordinates (4, 0), (-4, 0), (0, 4),
(0, -4), (1, 2), (1, -2), (3, 3), (3, -3), (2, 1), (2, -1), (-1, 2), (-1, -2), (-3, 3), (-3, -3), (-2, 1), (-2, -1)
(b) Join the points to form an 8 pointed star.
2. (a) On a graph paper, draw the rectangles with corners at the following points with coordinates:
a) (-6, 6), (-5, 6), (-5, 4), (-6, 4)
b) (-2, 1), (-3, 1), (-3, 3), (-2, 3)
c) (3, 1), (3,3), (4, 3), (4, 1).
d) (10, 1), (10, 3), (9, 3), (9, 1)
e) (12, 4), (13, 4), (13, 6), (12, 6)
(b) Join the points with coordinates:
(1, -5), (1, -1), (2, 0), (5, 0), (6, -1), (6, -5)
Sub-topic 4.2: Plotting Polygons (shapes)
Here we look at polygons plotted on coordinate axes, but first, recall
the names of polygons.
Names of polygons
Note:
In a regular polygon:
(a) all the sides are the same.
(b) all the angles are of the same size.
Activity 4.2: The line AB is one side of a square
What are the possible coordinates of the corners of the square?
Exercise
1. In each case the coordinates of 3 corners of a square are given.
Find the coordinates of the other corner.
(a) (2, -2), (2, 3) and (-3, 3)
(b) (2, 3), (3, 4) and (1, 4)
(c ) (2, 2), (4, 4) and (4, 0)
(d) (-6, 2), (-5, -5) and (1, 3)
(e) (-5, -2), (-2, -1), and (-1, -4)
2. The coordinates of 3 corners of a rectangle are given below. Find
the coordinates of the other corner of each rectangle.
(a) (-4, 2), (-4, 1) and (6, 1)
(b) (0, 2), (-2, 0) and (4, -6)
(c ) (-4, 5), (-2, -1) and (1, 0)
(d) (-5, 1), (-2, 5) and (6, -1)
3. (a) The coordinates of 2 corners of a square are (-4, 4) and (1, -1).
Explain why it is possible to draw three different squares using these two points.
(b) Draw the three different squares.
(c ) If the coordinates of the corners had been (-5, 1) and (1, 3) would it still be possible to draw 3 squares? Draw the possible squares.
4. Half of a heptagon with one line of symmetry can be drawn by joining the points with coordinates: (2, 4), (-2, 1), (-2, -1), (0, -3) and (2, -3). Join the coordinates. You have drawn one half of the heptagon. Complete the heptagon. Write down the coordinates.
Sub-topic 4.3: Use of Appropriate Scale for Given Data
Activity4.3: Plot the following points on the axes: (5, 50), (10,100), (15,150), (20,200), (35, 350)
Do you realize that on the horizontal axis there are 5 units for each space?
On the vertical axis there are 50 units for each space. So, what is the scale for the axes?
Exercise
1. For each part, draw a pair of axes with suitable scales and plot the points:
(a) (1, 15); (4, 35); (8, 45)
(b) (15, 100); (35, 500); (40, 700)
2. Plot the points (2, 60); (4, 50); (0, 70); (7, 60)
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 big 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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