Topic 4: Rectangular Cartesian Coordinate in Two Dimensions

By the end of this topic, you will be able to:

• draw and label the cartesian plane
• identify the x and y axis
• read and plot points on the cartesian plane/ coordinate grid
• complete shapes on a coordinate grid
• choose and use appropriate scale for bivariate data

Keywords

• bi-variate data set
• cartesian
• cartesian plane
• coordinate grid
• ordered pair
• quadrant
• rectangular coordinate
• scale

Introduction

Imagine you’re to travel to Soroti from Kampala, how many kilometres would you travel to the East, then to the North? The Cartesian grid can help you identify a point from the origin. This grid specifies each point uniquely in a plane using a set of numerical coordinates.

The Cartesian plane was invented by René Descartes, who was a French Mathematician and Philosopher.

Drawing and Labelling a Cartesian Plane

The Cartesian coordinate system is a combination of two number lines, one horizontal and the other vertical. In the following activity, you will draw and label the Cartesian plane.

Activity 4.1 Drawing and labelling the Cartesian plane (work in groups)

What you need: pencil, ruler, Squared Paper.

What to do:

1. Draw a horizontal number line and mark it from -5 to 5.

2. Draw another vertical number line to cross the first one at the 0 mark.

3. Also label the second number line from -5 to 5.

4. Mark the vertical line as the y-axis and the horizontal line as the x-axis.

5. Present your work to the whole class

The coordinate plane is the platform on which graphing takes place. It is similar to a number line with two dimensions, the x-axis and the y-axis.

Reading and Plotting points on the Cartesian plane

You can use Cartesian coordinates to pinpoint where you are on a map. In the following activity, you will read and plot Cartesian coordinates of places on the map of Uganda.

Activity 4.2 Reading and Plotting points on the Cartesian plane (work in groups) What you need: pencil, pen, notebook.

What to do:

Study the figure below, a map of Uganda on a grid, and answer the questions that follow.

1. Write down the coordinates of the following places:

a) Arua b) Moroto c) Bukoba

d) Mt. Elgone) Kabale

2. Trace the figure and plot the following places at the coordinates indicated:

a) Ntusi (-2,-2) c) Jinja (1, 1) b) Kidepo N.P (3, 5)

3. Present your work to the whole class.

Exercise 4.1

Study the figure below and answer the questions that follow.

1. Identify and label the y and x-axes.

2. Write down the coordinates of the following features.

a) Mosque d) Market b) Church c) School

e) Hospital f) Station

3. A new student at school mistakenly moved 6 units east and 4 units south.

a) Where did he end up?

b) What is his position from home?

4. If you were the district planner where would you advise an investor to establish a fish factory and why?

Completing Shapes on a Coordinate Grid

Activity 4.3 Completing shapes on the coordinate grid (work in groups) What you need: graph paper/graph book, pen, pencil. What to do:

1. Plot the following points on a Cartesian plane:

a) A(-2, 2), B(+3, 3), C(+3, -1), D(-2, -2)

b) P(2, 2), Q(6, 2), M(3, 4) N(6, 4)

2. Name the figures formed when you join the following coordinates:

a) ABCD b) PQMN

3. If coordinates R(-2, 2) and T(2, 2) make a side of a square, look for the possible coordinates of the other corners S and P of the square.

4.What are the coordinates of the third point Z of an isosceles triangle given that the other vertices are X(2, 4) and Y(-3, -1).

5. Present your work to the whole class.

Example

Mulenga has a plot of land in the shape of a quadrilateral. With point P(-2, +2), Q(+5, +2), R(-2, -1) and S(+1, -1).

a) Represent Mulenga’s plot on a Cartesian graph

b) What is the name of the shape of Mulenga’s land? The shape of Mulenga’s piece of land is scalene trapezium.

Excercise 4.2

1. The corners of a building are A(-1, 4), B(5, 4), C(5, 1) and D(-1, 1).

a) Represent the points on a Cartesian plane.

b) Join the points to form a figure.

c) Name the figure formed.

d) Calculate the area of the figure formed.

2. Given that W(0, 3), X(3,0), Y(-1, -4) and Z(-4, -1) are table corners. Use a Cartesian grid to write the shape of the table.

3. Given that A(-3, -3), B(2,-3), C(2,-3) and D are vertices of a four-sided figure. a) Draw a grid and plot the points of the figure given.

b) Locate and identify the coordinates of point D to form a rectangle.

Choosing and Using Appropriate Scale for a Bi-variate Data Set

Imagine you have the height and foot length of all learners in your group. How can you use a Cartesian plane to represent that information? In the following activity, you will collect data on height and waist size of members in your group and plot them on a scatter graph.

Activity 4.4 Plotting a scatter graph (work in groups)

A Scatter Plot has points that show the relationship between two sets of data. In the activity above, each dot shows one person’s weight versus waist size. Example

Exercise 4.3

1. The heights and ages of six pupils have been plotted on the scatter graph. Scatter graph of foot length (cm) and height (cm).

a) Who is the tallest and how tall is the person?

b) Who has the same height in centimetres as Apio?

c) Who has the longest foot? d) How taller is Bob than Cherop?

2. The table below represents the heights and mass of students. Study it carefully and use it to plot a scatter graph.