How to use the geometric sketchpad to create a coordinate system in any direction

In mathematical drawing, custom coordinate systems are crucial. With Geometry Sketchpad, a powerful software, you can easily create a coordinate system in any direction. This article will introduce in detail the operation method of creating a coordinate system in any direction in the geometric sketchpad to help you easily solve the problem of coordinate system drawing.

1. Select [Point Tool] to draw point A and point B. Select point A, select the [Transform]-[Translation] command, and use the default parameter settings to obtain point A’. Select points A and A’ in turn, and select the [Construction]-[Draw a circle with the center of the circle and points on the circumference] command. Select A’ and press [Ctrl H] to hide point A’.

2. Select points A and B, and select the [Construction]-[Ray] command. Let the ray intersect the circle at point C. Draw ray CA such that CA intersects the circle at point D. Select point A and line segment AB, and select the [Construction]-[Perpendicular Line] command. Let the vertical line and the circle intersect at points E and F respectively.

3. Hide vertical line EF and ray CD, and construct rays AF, AE, and AD. Take points G, H, and I on rays AF, AE, and AD respectively, hide points C, and D, and rays AB, AD, AF, and AE to construct line segments HB and GI.

4. Draw a point J on line segment AB, double-click point A and set it as the mark center. Select point J, select the [Transform]-[Rotate] command, and use the default value options. Got point J’.

5. Select point B, select [Transform]-[Translation] command, set [Fixed Distance] to 0.5 cm, and use the default values ​​for the rest. This leads to point B’. Select points B and B’ in turn, select [Construction] - [Draw a circle with the center of the circle and points on the circumference] command to make the circle and line segment AB intersect at point K.

6. Double-click point B and mark B as the center. Select point K, select the [Transform]-[Translation] command, and set the angle rotation angle to 180 degrees. In this way, K’ point is obtained. Double-click point K’ to mark K’ as the center. Select point B, select the [Transform]-[Translation] command, and set the angle rotation angle to 15 degrees. Get point L. Double-click the line segment AB, mark the line segment AB as a mirror surface, select the point L, and select the [Transform]-[Reflection] command to obtain the point L’.

7. Select points L, L’, K’, select [Construction]-[Triangle Interior] command, and fill the triangle with blue. Right-click the triangle, select [Properties], and change the transparency to 100%.

8. Select points B’, L, L’, K, K’ and the circle passing B’, and select the [Show]-[Hide Object] command.

9. Repeat steps 6-8 and draw a blue arrow at point I. Select the circle with A as the center and select the [Show]-[Hide Circle] command.

10. Select the entire coordinate system and click the [Create New Tool] command under the [Custom Tool] button. Enter a name in the dialog box. There is a new line of commands in the lower-level menu. As long as you select this new command and drag the mouse on the drawing board, a rectangular coordinate system will appear, and the direction of the coordinates can be adjusted arbitrarily.

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