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Unit F4 Section 2
Coordinates

The coordinates of a point are written as a pair of numbers, (x, y), which describe where the point is on a set of axes.

The x-axis is always horizontal (i.e. across the page) and the y-axis always vertical (i.e. up the page).

The x-coordinate is always given first and the y-coordinate second.

Worked Examples

1

On a grid, plot the point A which has coordinates (–2, 4), the point B with coordinates (3, –2) and the point C with coordinates (–4, –3).

For A, begin at (0, 0), where the two axes cross.
Move –2 in the x direction.
Move 4 in the y direction.

Points B and C are plotted in a similar way.

For B, move 3 in the x direction and –2 in the y direction.

For C, move –4 in the x direction and –3 in the y direction.
2

Write down the coordinates of each place on the map of the island.

Lighthouse (7, 5)

Jetty (1, 3)

 ⎫
⎬
⎭ All coordinates positive

Church (3, −2)

Camp Site (1, −3)

 ⎫
⎬
⎭ Negative y-coordinates

Shop (−4, 2)

Telephone Box (−4, 1)

 ⎫
⎬
⎭ Negative x-coordinates

Café (−5, −2)

Lifeboat Station (−2, −2)

 ⎫
⎬
⎭ All coordinates negative

Exercises

Write down the coordinates of each point marked on the grid below.

A (, )

B (, )

C (, )

D (, )

E (, )

F (, )

G (, )

H (, )

I (, )

J (, )

K (, )

L (, )

The map shows some Australian towns and cities.

(a)

Write down the coordinates of Canberra, Brisbane and Perth.

Canberra (, )

Brisbane (, )

Perth (, )

(b)

A plane flies from the place with coordinates (–5, –6) and lands at the place with coordinates (–2, –1). From where does the plane take off and where does it land?

Take off:

Land:

(c)

A ship has coordinates (–5, 2) at the start of a voyage and coordinates (–6, –5) at the end. Where does it start and where does it finish?

Start:

Finish:

The positions of some of the tors (rocky outcrops) on Dartmoor in the south west of England are marked on the grid below.

(a)

Write down the coordinates of the following tors.

West Mill Tor (, )

Steeperton Tor (, )

Shelstone Tor (, )

Black Tor (, )

Dinger Tor (, )

(b)

The highest tor marked on the grid is Yes Tor. Write down the coordinates of this tor.

(, )
(c)

A boy and his dog walk from Oke Tor to Kitty Tor. Write down the coordinates of the point where they start and the point where they finish.

Start: (, )

Finish: (, )

(d)

Sourton Tor is the tor that is the farthest west on this grid. What are the coordinates of this tor?

(, )
(e)

Higher Tor is the tor that is farthest north. What are the coordinates of this tor?

(, )

Three corners of a square have coordinates (4, 2), (–2, 2) and (4, −4).

Draw a set of axes with x-values from –2 to 4 and y-values from −4 to 2.
Plot the three points and draw the square.

Write down the coordinates of the centre of the square.

(, )

Two corners of a rectangle have coordinates (–3, –1) and (–3, 3). The centre of the rectangle has coordinates (1, 1).

Plot the three points given and draw the rectangle.

Write down the coordinates of the other two corners of the rectangle.

(, ) and (, )

A set of axes are arranged so that the x-axis runs from west to east and the y-axis from south to north.

A ship is at the point A which has coordinates (4, 2).

(a)

How far south can the ship travel before its y-coordinate becomes negative?

units
(b)

How far west can the ship travel before its x-coordinate becomes negative?

units
(c)

If the ship travels SW, how far does it travel before both coordinates become negative?

units (to 2 d.p.)