Unit 5 Section 1 : Coordinates

Firstly, we recap the concept of ( x, y ) coordinates, illustrated in the following examples.

Example 1

On a set of coordinate axes, plot the points

A (2, 3), B (0, 4), C (–2, 3), D (–1, –2), E (–3, 0), F (2, –4)

The x-axis and the y-axis cross at the origin, (0, 0).
To locate the point A (2, 3), go 2 units horizontally from the origin in the positive x-direction and then 3 units vertically in the positive y-direction, as shown in the diagram.

Example 2

Identify the coordinates of the points A, B, C, D, E, F, G and H shown on the following grid:

A (3, 1)
B (0, 2)
C (–2, 2)
D (–3, 0)
E (–2, –4)
F (0, –2)
G (2, –3)
H (2, 0)

Example 3

Marc has ten square tiles like this:
Marc places all the square tiles in a row.
He starts his row like this:
For each square tile he writes down the coordinates of the corner which has a .
The coordinates of the first corner are (2, 2).
(a) Write down the coordinates of the next five corners which have a .
(b) Look at the numbers in the coordinates. Describe two things you notice.
(c) Marc thinks that (17, 2) are the coordinates of one of the corners which have a . Explain why he is wrong.
(d)
Sam has some bigger square tiles, like this:
She places them next to each other in a row, like Marc's tiles.
Write down the coordinates of the first two corners which have a .

Exercises

Question 1
Write down the coordinates of the points marked on the following grid:
A
B
C
D
E
F
G
H
Question 2
On a set of coordinate axes, with x values from –5 to 5, y values from –5 to 5, plot the following points:

A (2, 4), B (1, 2), C (–2, 5), D (–3, –3),
E (–2, –4), F (0, –3), G (–4, 0), H (2, –3)

What can you say about A, B and E?
Question 3
On a suitable set of coordinate axes, join the points (3, 0), (0, 4) and (–3, 0).
What shape have you made?
Question 4
Three corners of a square have coordinates (4, 2), (–2, 2) and (4, –4).
Plot these points on a grid, and state the coordinates of the other corner.
Remaining corner: (,)
Question 5
Three corners of a rectangle have coordinates (4, 1), (–2, 1) and (–2, –3).
Plot these points on a grid and state the coordinates of the other corner.
Remaining corner: (,)
Question 6
Two adjacent corners of a square have coordinates (– 1, 1) and (2, 1).
(a)What is the length of a side of the square?
units
(b)What are the possible coordinates of the other two points?
,
Question 7
Daniel has some parallelogram tiles. He puts them on a grid, in a continuing pattern. He numbers each tile.
The diagram shows part of the pattern of tiles on the grid.
Daniel marks the top right corner of each tile with a .
The coordinates of the corner with a on tile number 3 are (6, 6).
(a)
What are the coordinates of the corner with a on tile number 4 ?
(b)
What are the coordinates of the corner with a on tile number 20 ?
because both coordinates are equal to double the tile number
(c)
Daniel says: "One tile in the pattern has a in the corner at (25, 25)."
Is Daniel right?
Daniel is wrong because 25 is an odd number and all the corners with a have even numbers.
(d)
Daniel marks the bottom right corner of each tile with a . Copy and complete the table to show the coordinates of each corner with a .
Tile NumberCoordinates of the Corner with a
1(2, 1)
2
3
4
(e)
Complete the statement:
'Tile number 7 has a in the corner at ( , ).'
(f)
Complete the statement:
'Tile number has a in the corner at (20, 19).'
Question 8
A robot can move about on a grid. It can move North, South, East or West. It must move one step at a time.
The robot starts from the point marked on the grid below.
It takes 2 steps.
1st step: West
2nd step: North
It gets to the point marked .
(a)
The robot starts again from the point marked .
It takes 2 steps.
1st step: South
2nd step: South
Mark the point it gets to with a on the grid below.
(b)
The robot always starts from the point marked . Find all the points the robot can reach in 2 steps. Mark each point with a on the grid below.
(c)
Another robot always starts from the point marked on this grid.
It takes 3 steps.
1st step: South
2nd step: West
3rd step: West
It gets to the point marked . The robot starts again from the point marked .
Complete the table to show two more ways for the robot to get to the point marked in 3 steps.
1st step South West
2nd step West
3rd step West