


Want to accurately measure the distance between the midpoint of the geometric sketchpad and the path? PHP editor Banana has brought you a practical tutorial, which introduces in detail the "point value measurement" function of using the geometric sketchpad, and guides you step by step to obtain accurate measurement results. Through this tutorial, you can easily master the method of measuring point values in the geometric sketchpad, solve measurement problems, and explore the mysteries of geometry.
The path of the point on the path refers to: line segment, ray, straight line, circle, arc, interior (boundary), trajectory and function image, etc., which are explained in detail below.
1. Point on the line segment
As shown in the figure below, point C is on the line segment AB. When we select point C, click [Measurement] - [Point Value], you can Get the value inside a circle. By measuring the ratio of point A, point B and point C, we can see that the ratio of the value of point C on AB to the length of the entire line segment is equal. Therefore, we can understand the value of the point on the line segment as: This point The ratio of the distance to the starting point of the line segment (i.e. the point drawn first) to the length of the entire line segment.
2. Point on the ray
As shown in the figure below, point C is on the ray AB. When we select point C, click [Measure]——[ point value], you can get a value in the range of [0,∞]. By measuring the ratio of point A, point B and point C, we can see that the value and ratio of point C on AB are equal. Therefore, we can understand the value of the point on the ray as: from this point to point A ( That is, the ratio of the distance from the starting point of the ray to the length of AB.
3. The point is on the straight line
As shown in the figure, point C is on the straight line AB. When we select point C, click [Measure] - [ point value], you can get a value in the real range. By measuring the ratio of point A, point B and point C, we can see that the value and ratio of point C on AB are equal. Therefore, we can understand the value of the point on the ray as: point A, point B and Ratio of point C.
4. Point on the circle
As shown in the figure below, point A is on the circle O. When we select point A, click [Measure] - [ Point value], you can get a value in the range of 0-1. We can understand it as: draw a horizontal straight line through point O, and draw the right intersection point of the horizontal straight line and the circle (point B in the figure), then the value of the point is the ratio of arc BA to the circumference of the circle.
5. Point on the arc
As shown in the figure below, point C is on the arc AB. When we select point C, click [Measure]——[ Point value], you can get a value in the range of 0-1. We can understand it as: the value of a point is the ratio of arc AC to arc AB.
6. The point is inside the polygon (that is, on the boundary)
As shown in the figure below, point E is on the boundary of a quadrilateral ABCD. When we select point E, Click [Measurement] - [Point Value] to get a value in the range of 0-1. We can understand it as: the ratio of the distance traveled by point E from the starting point inside the quadrilateral to point E and the perimeter of the polygon (the first selected point is the starting point of the polygon, where the distance traveled between point E and the starting point is the same as the order in which the polygon is constructed. Related (divided into clockwise and counterclockwise), therefore, when point E is at the starting point of the polygon, the value of the point is 0).
In the above picture, I constructed two quadrilaterals. The first one is point ABCD, and the second one is point BCDA. You can see that point E is in the two polygons. The values of the points on are different.
7. Points on trajectories and function images
Through the above six detailed introductions, I believe you have an understanding of the value of points. Then, points on trajectories and function images have different types. Many, different construction methods lead to different point values. I won’t go into details here. You can understand it by yourself based on the above method.
The above is the detailed content of How to measure the value of a geometry sketchpad point when on a path. For more information, please follow other related articles on the PHP Chinese website!

Microsoft PowerToys is free. This collection of tools developed by Microsoft is designed to enhance Windows system functions and improve user productivity. By installing and using features such as FancyZones, users can customize window layouts and optimize workflows.

ThebestalternativestoPowerToysforWindowsusersareAutoHotkey,WindowGrid,andWinaeroTweaker.1)AutoHotkeyoffersextensivescriptingforautomation.2)WindowGridprovidesintuitivegrid-basedwindowmanagement.3)WinaeroTweakerallowsdeepcustomizationofWindowssettings

Microsoft PowerToys does not require a license and is a free open source software. 1.PowerToys provides a variety of tools, such as FancyZones for window management, PowerRename for batch renaming, and ColorPicker for color selection. 2. Users can enable or disable these tools according to their needs to improve work efficiency.

Microsoft PowerToys is completely free. This tool set provides open source utilities that enhance Windows operating system, including features such as FancyZones, PowerRename, and KeyboardManager, to help users improve productivity and customize their operating experience.

PowerToys is not the default component of Windows 11, but a set of tools developed by Microsoft that needs to be downloaded separately. 1) It provides features such as FancyZones and Awake to improve user productivity. 2) Pay attention to possible software conflicts and performance impacts when using them. 3) It is recommended to selectively enable the tool and periodically update it to optimize performance.

The way to download Microsoft PowerToys is: 1. Open PowerShell and run wingetinstallMicrosoft.PowerToys, 2. or visit the GitHub page to download the installation package. PowerToys is a set of tools to improve Windows user productivity. It includes features such as FancyZones and PowerRename, which can be installed through winget or graphical interface.

PowerToys is a free collection of tools launched by Microsoft to enhance productivity and system control for Windows users. It provides features through standalone modules such as FancyZones management window layout and PowerRename batch renaming files, making user workflow smoother.

PowerToys needs to be run in the background to achieve its full functionality. 1) It relies on system-level hooks and event listening, such as FancyZones monitoring window movement. 2) Reasonable resource usage, usually 50-100MB of memory, and almost zero CPU usage when idle. 3) You can set up power-on and use PowerShell scripts to implement it. 4) When encountering problems, check the log files, disable specific tools, and ensure that they are updated to the latest version. 5) Optimization suggestions include disabling infrequently used tools, adjusting settings, and monitoring resource usage.


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