vms Year 8 Mathematics Co-Ordinates

Learning Intentions Pupils should be able to use and plot co-ordinates in all 4 quadrants use negative numbers in context find the mid- point of a line Solve problem using co-ordinates

Co-Ordinate Systems Used to specify a location Latitude and Longitude Ordinance Survey 6 figure Grid system Post Codes GPS Cartesian Co-ordinates

Devised by René Descartes ( ) Two axes at right angles Y-axis is vertical X-axis is horizontal The point (0, 0) is called the Origin. Y’s Up and X is across

X and Y Co-ordinates Co-ordinates are written as two numbers in brackets separated by a comma. For example (2, 4) and (8, 7) The first number refers to the x-ordinate The second number refers to the y-ordinate Together they are called co-ordinates

Plotting Co-ordinates When plotting co-ordinates we always start from the origin To plot the point (2, 3) we start at the origin and move two squares in the x (horizontal) direction and then three square in the y (vertical) direction. To plot the point (8, 9) we start at the origin and move eight squares in the x (horizontal) direction and then nine square in the y (vertical) direction.

Mid-Point The mid-point of a line is the point in the middle of the line You can find the co-ordinates of the mid-point by finding the average of the x ordinates at each end of the line and the y ordinates at each end of the line.

Finding the mid-point Find the mid-point of the line from (2, 4) to (6, 2) x ordinate = = 4 y ordinate = = 3 Co-ordinates of mid-point = (4, 3)

Horizontal Lines For a horizontal line, all the points on the line have the same y ordinate.

Vertical Lines For a vertical line, all the points have the same x ordinate

Properties of Shapes Quadrilateral Four sides Trapezium Four sides One pair of parallel sides Parallelogram Four sides Two pairs of parallel sides Opposite sides equal

Properties of Shapes Rhombus Four sides Opposite sides parallel All sides equal Rectangle Four sides Opposite sides parallel Four right angles

Properties of Shapes Square Four sides Opposite sides parallel Opposite sides equal Four right angles Kite Four sides Adjacent sides equal

The Four Quadrants Extending the x and y axes beyond the origin gives the negative scales. The areas of the graph between axes are called quadrants. So now we have four quadrants in total. Co-ordinates in these quadrants are still described in terms of x and y. But now we can have negative values for x, y or both. For example in the below: The coordinates of A are (-2, 3). The coordinates of B are (-3, -4).

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