In the applet window below,[br][br]1) Construct a line. [br]2) Construct a line parallel to this given line. [br]3) Use the SLOPE tool [icon]/images/ggb/toolbar/mode_slope.png[/icon] to measure and display the slopes of both lines.
Select the MOVE tool again. Move any of the first 2 points you plotted (in step 1) around. What do you notice? [br]
If two distinct (non-vertical) lines are drawn in the coordinate plane, then they have the same slope.
5) Construct a line that is perpendicular to the first line you drew that passes through any other point [br] It doesn't matter where you choose to position this line. [br][br]6) Use the SLOPE tool [icon]https://www.geogebra.org/images/ggb/toolbar/mode_slope.png[/icon] to measure and display the slope of this perpendicular line. [br][br][color=#0000ff]Further directions can be found below the applet.[/color]
7) The label for the slope of the first line should be [math]m[/math]. [br] The label for the slope of the perpendicular line should be [math]m_2[/math]. [br] Go to the algebra view (left). In the next input line, type (w/o the " "): "FractionText([i]m[/i])". [br] In the next input line, type (w/o the " "): "FractionText[math]\left(m_2\right)[/math]". [br] If you so choose, you can choose to show these text boxes in the graphics window.
Move any one of the first 2 points you plotted (in step 1) around. What do you notice about the slope of this line and the line perpendicular to it? Explain.
If two (non-horizontal and non-vertical) lines drawn in the coordinate plane are perpendicular, then their slopes multiply to -1. We can also say their slopes are opposite reciprocals. [br][br][b]Teachers:[/b][br]Here is one means for students to actively discover these relationships for themselves.
[color=#0000ff]When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet. [/color]