Find CoOrdinates of Points Plot points on a

Find Co-Ordinates of Points Plot points on a Cartesian Plane. The Cartesian Plane is also called the Coordinate Plane.

Cartesian Plane ¡ ¡ ¡ A Cartesian Plane is like a spider web. But all the lines are straight and the blocks are square. The Cartesian Plane does not end.

Cartesian Plane ¡ ¡ ¡ A Cartesian Plane is like a spider web. But all the lines are straight and the blocks are square. The Cartesian Plane does not end.

Origin on the Cartesian Plane ¡ ¡ Draw a horizontal number line. Draw a vertical number line. The point where the lines cross is called the Origin. Label the origin O. O

The x and y Axis y ¡ ¡ The horizontal number line is the x axis. The vertical number line is the y axis. O x

The x and y Axis y ¡ 5 ¡ Write the scale 4 on the x axis. 3 2 1 O Write the scale on -5 -4 -3 -2 -1 -1 1 the y axis. -2 -3 -4 -5 2 3 4 5 x

Quadrants on the Cartesian Plane y ¡ ¡ ¡ The x and the y axis divide the plane into four quarters. The quarters are called: Quadrant 1 2 3 4 Label them anti-clockwise 5 4 3 Quadrant 2 Quadrant 1 2 1 O -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 Quadrant 3 Quadrant 4 -3 -4 -5

Points on the Cartesian Plane y ¡ 5 4 ¡ There are millions of points 3 on the Cartesian 2 Plane. 1 O Let’s have a look -5 -4 -3 -2 -1 -1 1 at some of them. -2 -3 -4 -5 2 3 4 5 x

Points on the Cartesian Plane y ¡ 5 4 ¡ We have to be able to describe 3 exactly where 2 each point is. 1 O If a fly gets stuck -5 -4 -3 -2 -1 -1 1 in the web, the -2 spider must know where to find it. -3 -4 -5 2 3 4 5 x

Points on the Cartesian Plane ¡ The spider starts at the origin. 5 4 3 2 1 How far must it move -5 -4 -3 -2 -1 -1 along the x axis until it -2 is exactly under the fly? -3 -4 -5 y 1 2 3 4 5 x

Points on the Cartesian Plane ¡ How far must the spider move up to get to the fly? 5 4 3 2 1 To get to the fly the spider moved 2 horizontally and 4 -5 -4 -3 -2 -1 -1 vertically. We write this as (2, 4). -2 (2, 4) are the co-3 ordinates of the point -4 where the fly is. (2, 4) means move 2 horizontal and 4 vertical. -5 y (2, 4) 1 2 3 4 5 x The fly is at the point (2, 4)

Points on the Cartesian Plane ¡ What is the x coordinate of the point where the fly is? 5 4 3 2 1 The spider moved 4 units along the x axis. -5 -4 -3 -2 -1 -1 The x co-ordinate is 4. -2 -3 -4 -5 y 1 2 3 4 5 x

Points on the Cartesian Plane ¡ What is the y coordinate of the point where the fly is? 5 4 3 2 1 The spider moved 3 -5 -4 -3 -2 -1 units vertically. -1 The y co-ordinate is 3. (4, 3) are the co-ordinates of the fly. (4, 3) are also called an ordered pair. -2 -3 -4 -5 y (4, 3) 1 2 3 4 5 x The fly is at the point (4, 3)

Directions along the x-axis y ¡ 5 4 ¡ Going to the right on the x-axis is 3 going in a positive 2 direction. 1 O Going to the left on -5 -4 -3 -2 -1 -1 1 2 3 4 5 x the x-axis is going in -2 a negative direction. Negative direction Positive direction -3 -4 -5

Directions along the y-axis y ¡ 5 4 ¡ Going up along Positive the y-axis is going 3 direction in a positive 2 direction. 1 O -5 -4 -3 -2 -1 1 2 3 4 5 x Going down along -1 the y-axis is going in -2 a negative direction. Negative direction -3 -4 -5

Points in the Second Quadrant ¡ ¡ ¡ What is the x coordinate of the point? 5 4 3 2 1 The spider moves 4 -5 -4 -3 -2 -1 units in a negative -1 direction. -2 The x co-ordinate is -4. -3 -4 -5 y 1 2 3 4 5 x

Points in the Second Quadrant ¡ ¡ What is the y coordinate of the point? (-4, 2) 5 4 3 2 1 The spider moves 2 -5 -4 -3 -2 -1 units in a positive -1 direction. -2 The y co-ordinate is 2. -3 The ordered pair is: -4 (-4, 2) -5 y 1 2 3 4 5 x

Points in the Third Quadrant ¡ ¡ ¡ What is the x coordinate of the point? 5 4 3 2 1 The spider moves 2 -5 -4 -3 -2 -1 units in a negative -1 direction. -2 The x co-ordinate is -2. -3 -4 -5 y 1 2 3 4 5 x

Points in the Third Quadrant ¡ ¡ What is the y coordinate of the point? 5 4 3 2 1 The spider moves 4 -5 -4 -3 -2 -1 units in a negative -1 direction. -2 The y co-ordinate is -4. -3 The ordered pair is: (-2, -4) -4 (-1, -4) -5 y 1 2 3 4 5 x

Points in the Fourth Quadrant ¡ What is the x coordinate of the point? 5 4 3 2 1 The spider moved 4 -5 -4 -3 -2 -1 units in a positive -1 direction along the x -2 axis. The x co-ordinate is 4. -3 -4 -5 y 1 2 3 4 5 x

Points in the Fourth Quadrant ¡ What is the y coordinate of the point? 5 4 3 2 1 The spider moved 4 -5 -4 -3 -2 -1 units in a negative -1 direction along the y -2 axis. The y co-ordinate is -4. -3 The ordered pair is: -4 (4, -4) -5 y 1 2 3 4 5 x (4, -4)

Exercise Instructions ¡ In your exercise book, write down the co-ordinates of the points A, B, C and D. 5 4 3 2 1 Write each answer as the letter, followed by -5 -4 -3 -2 -1 -1 the ordered pair or co-2 ordinates. e. g. A(4, 3) -3 -4 -5 y A 1 2 3 4 5 x

Exercise ¡ In your exercise book, write down the co-ordinates of the points A, B, C and D. B 5 4 3 2 1 Write each answer as the letter, followed by -5 -4 -3 -2 -1 -1 the ordered pair or co-2 C ordinates. -3 -4 -5 y A 1 2 3 4 5 x D

Check your Answers ¡ A(5, 4) ¡ B(-4, 4) ¡ C(-3, -2) ¡ D(3, -4) B 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 C -3 -4 -5 y A 1 2 3 4 5 x D

Plot a Point on a Graph ¡ ¡ ¡ Plot the point A(-5, 4) Start at the origin. Measure the x coordinate along the x axis. Measure the y coordinate along the y axis. Mark the point. A(-5, 4) 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 y 1 2 3 4 5 x

Exercise ¡ ¡ In your exercise book, draw the grid, with x and y axes, shown on the right. Plot the following points on your grid: l A(3, 1) l B(-2, 4) l C(-4, -3) l D(1, -4) 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5 y 1 2 3 4 5 x

Check your Answers ¡ ¡ Check that your points are in the same places as the points shown here. Points: l A(3, 1) l B(-2, 4) l C(-4, -3) l D(1, -4) B 5 4 3 2 1 y -5 -4 -3 -2 -1 1 -1 -2 -3 C -4 D -5 A 2 3 4 5 x

Well Done! ¡ ¡ ¡ You have learned the basics of plotting points on a Cartesian plane. Make sure you fully understand the basics. To draw line graphs you need to know the basics.