How to measure the value of a geometry sketchpad point when on a path

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.

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