AS+2.1+Co-ordinate+Geometry

2.1 Achievement Standard
An using Co-ordinate Geometry skills eg gradient, distance, parallel and perpendicular lines.

You must know the difference between the different triangles
 * equilateral (all sides have the same length)
 * isosceles (two sides have the same length)
 * scalene (no sides have the same length)
 * right-angled triangle (has a 90 degree angle)
 * isosceles, right-angled triangle (has two sides equal as well as a 90 degree angle)

Likewise you must know the difference between the different four-sided shapes. Have a look at this (thanks Mrs Ellena!!) for more information about the different quadrilaterals and triangles and their properties.

While we're talking about quadrilaterals, click on this little exercise:

Use your mouse to move each of the corners, or the sides, and see if these shapes really are squares after all, what are they if they're not squares? - and maybe, if you'd like to play to around with geogebra (which is a free-to-dowload geometry package), see if you can work out how they've been constructed.

Here is a sample of what you can expect in the way of an for this topic. (Thanks again Mrs Ellena!!) Remember to do midpoint (if appropriate), distance and gradient as well as put together a sensible conclusion (vital!!) with a reason eg "it is a parallelogram because ......." Here is a hand-written for this problem.

Here is. Don't forget to name the thing you are calculating, show your calculations, say what your answer means eg two sides are parallel or of equal length etc.



The only formula on the official sheet is


 * y - y1 = m(x - x1) **

which is the one to use when you're trying to work out the equation of a line. It involves the gradient, m, and a point that the line goes through, called (x1, y1).

We will be looking to see if you are able to work with gradient, midpoint and distance. Not just one of them - you have to practise until you feel confident with each of these three things. Make sure you work through the practice assessment (underlined a couple of paragraphs up from here) and are familiar with the three and four sided shapes and be happy working in that context. And, of course, you must solve the problem given to you, ie answer the question, reach a conclusion.

Ask for help if you need it.