In Euclid's Elements, a point is defined as "that which has no part". It indicates that Euclid will be treating a point as having no width, length, or breadth, but as an indivisible location When the analytical geometry was theorized, it became possible to refer to this position through coordinates. (Based on the Brazilian portuguese entry - wikipedia source) [br]
[b]- [/b]Select the[b] POINT tool (Window 2)[/b] and draw some points in the preview window, clicking once to generate it. [list][*] You can name or label the points drawn. 2 ways you can make this: Either by typing the letter right after the object is drawn (point, line or circle) or by right-clicking and choosing the option "Show label". [/*][*]You can rename the point by right clicking it and choosing the option "Rename". [/*][/list][b]Notes[/b]: 1) Always name the object (point, line or circle) that you drawn. This will make it easier when you want to select it. 2) By convention, we use uppercase letters to label points and lowercase letters to label straight lines. You can move the point. In order to do this: [br]-Select the[b] MOVE tool (Window 1)[/b]. Click, hold and drag the point.[br][b]Save the construction.[/b]
It is where lines cross over (where they have a common point).
[b]- [/b]Select the[b] INTERSECT tool (Window 2)[/b] and create the intersection point of the intersecting objects. [b]Note[/b]: 1) You can draw a point by either pointing the cursor directly at the intersection point or by clicking on the two intersecting objects. You can move objects around and observe the points of intersection. In order to do this, select the[b] MOVE tool (Window 1)[/b]. Click, hold and drag the objects.[br][b]Save the construction.[/b][br]
Podemos definir o ponto médio como o ponto que divide o segmento de reta exatamente no meio tendo dois novos segmentos iguais. (fonte: wikipédia)
- Select the COMPASS [b]tool (Window 4)[/b]. Then click on the line of the CD segment (It represents the opening length of the compass) and then on the point [b]A [/b].Then, click on the line of the CD segment (It represents the opening length of the compass) and then on the point [b]B.[br]- [/b]Select the [b]INTERSECT (Window 3)[/b] and mark the intersections [b]E[/b] and [b]F [/b]of the two circles.[br]- Select the [b]SEGMENT tool (Window 4)[/b] and draw the segment with[b] E [/b]and [b]F[/b].[br][b]-[/b]Select the [b]INTERSECT tool (Window 3) [/b]and mark the intersection of segments [b]AB [/b]and [b]EF[/b]. Change the point name to [b]M[/b]. [br]- Select the [b]SHOW/HIDE OBJECT tool (Window 6)[/b] and hide the circles and the segment [b]EF[/b], leaving only the segment [b]AB[/b] and point [b]M.[/b] [br][b]NOTE[/b]: you can hide the objects by clicking on them with the right click and choosing the "Show object" option. [br]- Select the [b]DISTANCE OR LENGTH tool (Window 7)[/b] and click on [b]A[/b] and then on [b]M.[/b] Then click on [b]B[/b] and[br]then on [b]M[/b]. What do you see? What is a “Midpoint”? Points [b]A[/b] and [b]B[/b] are said to be symmetric in relation[br]to point [b]M[/b], which is considered the center of symmetry. [br]- Select the [b]MOVE tool (Window1)[/b] and move point [b]A [/b]or [b]B.[/b] Observe. Save the construction.[br]
What is explanation for the construction? That is, how to show that point M is in fact a midpoint?
Move points C or D, increasing and decreasing the opening of the compass. What is the length limit for point M to exist?
If there was no segment CD, would it be possible to build the midpoint with the compass tool?[br][br][br]