Detailed steps for constructing an ellipse using ellipse definition in Geometry Sketchpad

Question: How to construct an ellipse using the ellipse definition in the Geometry Sketchpad? Geometry Sketchpad is a software widely used in mathematics education. Its ellipse definition function can be used to construct precise ellipses. This guide walks through the steps of constructing an ellipse using the ellipse definition in Geometry Sketchpad, including setting the focus, major axis length, and minor axis length. By reading the following content, you will master the principles of ellipse construction and be able to easily draw accurate ellipses in Geometry Sketchpad.

1. Click the [Circle Tool], draw a circle at an appropriate position on the drawing board, and change the label of the center of the circle to F1. Click [Point Tool], draw any point C on the circle, select point F1 and point C at the same time, execute the [Construct]-[Line Segment] command to construct the line segment F1C. Click [Point Tool] and draw a point F2 on line segment F1C.

2. Draw any point E on the circle, and construct line segments EF1 and EF2. Select the line segment EF2 and execute the [Construction]-[Midpoint] command to construct the midpoint F of the line segment EF2.

3. Select line segment EF2 and point F, execute the [Construction]-[Perpendicular Line] command to construct the vertical bisector j of line segment EF2. Select the line segment EF1 and the straight line j at the same time, select the [Construction]-[Intersection Point] command to construct the intersection G of the line segment EF1 and the straight line j.

4. Select point G and point E (point E is called the relevant point of point G. If the position of point G is changed, the position of point E will also change), select [ Structure]-[Trajectory] command can draw an ellipse. Drag point B and point F2 to change the shape of the ellipse.

5. Execute the [File]-[Save] command.

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