Unit 3 Section 4 : Coordinates

Now that negative numbers have been introduced, we can start to use graphs with coordinate axes which have both positive and negative numbers on them. The negative numbers appear to the left of and below the centre of the graph (the origin). The positive numbers are to the right of and above the origin, as before.

The coordinates of point A are ( - 4 , 2 ). This can be explained as follows: Look at the dotted lines from the point A to to the two axes. They meet the x-axis at - 4 and the y-axis at 2, so the coordinates of A are ( - 4 , 2 ). Check for yourself that the coordinates of the point B are ( - 2 , - 4 ). Remember the x-coordinate always appears first. Some people prefer to think of the negative coordinates as going in the opposite direction, starting from the origin; a negative x-coordinate goes left instead of right and a negative y-coordinate goes down instead of up. You may find it helpful to think about it in this way.

Example Question

Practice questions Work out the answer to each of these questions then click on the button marked to see whether you are correct. (a) What are the coordinates of point B? (b) Which point has coordinates ( 3 , -4 )? (c) Is there a point plotted at coordinates ( 1 , - 1 )?

Exercises

Question 1
Look at the map of Paradise Island on the grid below and answer the questions on the right.

Fill in the coordinates of: (a) the Lighthouse ( , ) (b) the Pilot Boat ( , ) (c) Parrot Rock ( , ) (c) Banana Reef ( , )

Question 2 The map below shows another small island.

(a) What are the coordinates of: the cafe ( , ) the beach shop ( , ) the hotel ( , ) the campsite ( , ) the swimming pool ( , ) (b) Nisha moves from the place with coordinates ( - 3 , - 5 ) to the place with coordinates ( - 5 , 4 ). Where did she start and finish? Start : Light House Camp Site Cafe Landing Jetty Food Store Post Office Hotel Tennis Court Beach Shop Finish : Light House Camp Site Cafe Landing Jetty Food Store Post Office Hotel Tennis Court Beach Shop

In the next question you are going to plot some points on a set of axes. You click on the graph to plot a point using the coordinates in the table on the left. Then you check to see if you have plotted the point correctly by clicking on the button. If you plotted the point correctly, it will be ticked and will appear. If you see a cross on the point then you have made a mistake and must try again. You can remove points you have plotted incorrectly by clicking on them for a second time.

Question 3
Plot the sixteen points in the table below on this graph:

Points Check it! Points Check it! Points Check it! Points Check it! ( 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 )

Question 4
The picture below shows a giant chess board that has been drawn on the surface of a playground.
An x-axis and a y-axis have been marked on with each going from - 8 to + 8.

(a) What are the coordinates of the centre of the square that is the wrong colour? ( , ) (b) John always faces in the same direction as the y-axis. When he stands at the point with coordinates ( 0 , 7 ), he has his left foot on a white square and his right foot on a black square. Describe where John's feet are if he stands at: ( 2 , 5 ) Both feet on black Left foot black / right foot white Left foot white / right foot black Both feet on white ( - 5 , 3 ) Both feet on black Left foot black / right foot white Left foot white / right foot black Both feet on white ( 6 , - 3 ) Both feet on black Left foot black / right foot white Left foot white / right foot black Both feet on white ( - 1 , - 7 ) Both feet on black Left foot black / right foot white Left foot white / right foot black Both feet on white ( - 2 , 3 ) Both feet on black Left foot black / right foot white Left foot white / right foot black Both feet on white