# Lengths and Mid-points of Line Segments applet

My new applet on Coor­di­nate Geom­e­try con­cen­trates on two impor­tant skills for post-16 maths, espe­cially for UK AS lev­els Core 1 and 2.

## Lengths of Line Segments

This topic often seems to be the first use­ful math­e­mat­i­cal appli­ca­tion of the Pythago­ras Rule (Pythagorean The­o­rem) that kids come across. Ear­lier the focus is on con­trived right-angled tri­an­gles. How many of them are going to find the height or the guy-length of a flagpole?!

$d = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2}+{{\left( {{y_2} - {y_1}} \right)}^2}}$

It also encour­ages stu­dents to cal­cu­late by using a for­mula rather than a graph — you don’t need to draw or even imag­ine the triangle.

## Mid-points of Line Segments

Once again a sim­ple idea, but one which allows stu­dents quickly to ditch the dia­grams in favour of an easily-applied formula.

$P = \left( {\frac{{{x_2} + {x_1}}}{2},\frac{{{y_2} + {y_1}}}{2}} \right)$

Pretty soon the idea that the coor­di­nates are just the means of the x- and y–val­ues and it is this rather than the dia­grams which sticks in the stu­dents’ minds.

## So why ..

So why haven’t I given the for­mu­lae in the applet? This is because of a basic premise of Wal­do­maths — allow stu­dents to see things for them­selves. This way the for­mula seems almost obvi­ous and hence much eas­ier to remem­ber. Stu­dents also learn the tech­niques their own way and apply them with con­fi­dence, rather than the all-too-common rote learn­ing of for­mu­lae which leads to stress and errors.
Some­times it’s depress­ing to think that an applet which has taken me hours of work can achieve its aim within a few sec­onds of a stu­dents time. But then again that’s what Wal­do­maths is all about.

So why do I show the work­ing? Surely they need to able to work it out for them­selves? Well, you can turn the work­ing off!