In the applet below, notice that a [b]plane[/b] intersects (slices through) a sphere. [br][br]You can alter the position of the white plane by moving any 1 (or more) of the [b]LARGE POINTS [/b]this plane passes through. [br][br]You can control the size of the [b][color=#ff00ff]sphere[/color][/b] by using the [b]radius[/b] slider. [br][br]Directions: [br][br]1) Slide the [b]Slide Me! [/b]slider and carefully observe what happens. [br][br]2) After doing so, readjust the positions of the 3 blue points to create differently-positioned intersection. [br] The slide the [b]Slide Me! [/b]slider all the way back. [br][br]Repeat step (2) a few more times. Then answer the question that appears beneath the applet. [br][b][color=#1e84cc][br]To explore this resource in Augmented Reality, see the directions below this applet. [/color][/b]
How would you describe the cross section (intersection) of a plane and a sphere? Explain how what you observed helps support your assertion.
1) Open up GeoGebra 3D app on your device. [br][br]2) Go to the MENU (horizontal bars) in the upper left corner. Select OPEN. [br] In the Search GeoGebra Resources input box, type [b]wmahnyed[/b][br] (Note this is the resource ID = last 8 digits of the URL for this resource.)[br][br]3) In the resource that uploads, zoom in/out if needed.[br] [br] [b]While viewing in Augmented Reality: [/b] [br] [color=#9900ff]Move sliders a_1, b_1, c_1 to control the location of one purple point. [/color][br] [color=#ff7700]Move sliders a_2, b_2, c_2 to control the location of the orange point. [/color][br][color=#1e84cc] Move sliders a_3, b_3, c_3 to control the location of the blue point. [br][br][/color] And of course, slide the [b]SlideMe[/b] slider to animate.