Coordinates Coordinates on maps and plans Notes Grid

Co-ordinates

Co-ordinates on maps and plans

Notes • Grid references follow a system where two items of information are needed. Each place on a map has • A reference that relates to a horizontal line, usually on the bottom of the map. • A reference that relates to the vertical line, usually on the left hand side of the map. • The two references, taken together are called coordinates.

Notes (cont. . ) • To avoid confusion, we write down the horizontal reference first, and the vertical reference second. 5 4 Vertical 3 Line 2 1 A B C D Horizontal line

Practice • Pg 362

HW • Pg 77

Easy rules • • • X before Y Horizontal before Vertical Plot the points A ( -1, 3) B ( -2, -4) C ( 5, -2)

Positive and Negative Coordinates

Line Graphs • Graphs can also tell how one quantity changes as another one does. This is often done with a line graph.

Example • A graph shows what happens to the temperature of an egg over a period of 100 minutes. • The egg is taken from the refrigerator and placed in a saucepan of boiling water. It is then left to cool down on a kitchen bench. • What was the temperature inside the refrigerator? • How long was the egg in the saucepan of water? • What is the room temperature in the kitchen? • How long did it take the egg to cool down to room temperature, after it was removed from the boiling water?

Line Graph

Practice • Pg 377 – 27. 2

HW • 27. 2 Pg 80/ Pg 81

Distance –Time graphs • Another kind of graph shows travel or journey of some kind. • The time scale is on the horizontal scale. • The distance traveled is shown on the vertical scale.

• The graph shows a student’s journey one day. She went from home into town and back, via a bus stop. • How far is it from home to the bus stop? • How far did the student travel by bus into town? • How long did she have to wait at the bus stop? • How many minutes did she spend in town? • The bus travels 10 km in 10 minutes. How far would it travel in 60 minutes? • What is the speed of the bus in km/h ?

Practice • Pg 382 -27. 3

Co-ordinate Patterns • Sometimes there is a rule linking the x coordinate to the y co-ordinate. • Y=2 x • This means that the second number (y) in a pair of coordinates is 2 times the first number (x). x -2 -1 0 1 2 y Pair

Example • Plot some points that fit the rule • y = 3 x-1 x -1 0 1 2 3 y pair

Practice • Pg 385 – 27. 4

HW • Pgs 81, 82 , 83 (27. 4 only)

Graph Applications • Sometimes a graph is used to read off values. This is often faster than doing calculations. • Example: A full bucket of water with a hole at its side near the bottom.

Plot the graph with 2 points (extend both ways) • The rule for the amount of water in a leaking bucket is W = 10 -2 n (This means 10 - 2 x n) • W stands for the amount of water (measured in litres) • N stands for time in minutes since the bucket was full. • What is the value when n=1? • How much water is left in the bucket after 2 minutes?

Time versus Amount of water left in the bucket Amount of Water 10 2 0 5 Time in Minutes (N)

HW • Page 83