Package of problems

## Using GeoGebra

If a point is plotted on an axis using the “Point” tool:

then the point will be (automatically) constrained to lie on that axis.

Formulae can be entered in the input bar, so for example, if a point $A$ is created on the graph, we can create a formula for its $x$-coordinate:

xa = x(A)

and likewise for its $y$-coordinate:

ya = y(A)

Then let’s say we wished to draw the straight line with gradient $3$ through $A$. We could type into the input bar:

y - ya = 3(x - xa)

(using the $y-y_1=m(x-x_1)$ form for the equation of a straight line). The line should appear, and if the point $A$ is moved, the straight line will move with it.

These three lines of input could have been compressed to the single line:

y - y(A) = 3(x - x(A))

It is mostly a matter of preference which you choose to use.

For more details on using GeoGebra, see the Help section of the GeoGebra website (http://wiki.geogebra.org/en/Main_Page), which includes a tutorial and manual. Also, MEI has produced a series of GeoGebra guides, which can be found here.