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Slopes and Perpendiculars on the Casio ClassPad

There are a couple of ways to find the slope of a line in ClassPad.  First you have to select it.  Then you have to bring up the measure box by clicking on the Tab arrow at the extreme right of the button bar.   You can then look at either the equation of the line (in which case the slope is the coefficient of x) or you can have it display the slope directly.

    

We now create a perpendicular line through B.  To do this, we select B and the line and use the perpendicular construction:

    

We now look at the slope of this new line, and see that the product in the slopes is -1.

    

We can change the value of the slope of the original line by typing a new value into the measure box and pressing the Check button: try a few values and verify that the product of the slopes of the line with its perpendicular is always -1.

   

Why is this true?  A good way of seeing why is with a picture:

  

We have drawn a right angled triangle with its hypotenuse formed by the original line and its sides parallel with the x and y axes.  W see that the slope of the line is the expression:

We now rotate the triangle 90 degrees about B:

    

We can see that the gradient of the second line is (again rise over run):

Now as C’ and D’ are images under rotation of C and D, |C’B| = |CB| and |C’D’| = |CD|, hence we see that the product of the slopes is: