Does the origin belong to the axis?

Does the origin belong to the axis?

Belonging to both x-axis and y-axis

In the plane rectangular coordinate system, is the coordinate origin on the coordinate axis?

From a mathematical point of view: the coordinate origin is at the intersection of the coordinate axes
From the perspective of Surveying and mapping: if it is a reference coordinate system, the coordinate origin (the calculation point of coordinates) is not on the coordinate axis, such as China's 1954 Beijing coordinate system and 1980 Xi'an coordinate system, the former coordinate origin in the Soviet Union, the latter origin in Yongle Town, Jingyang, Shaanxi Province

In the plane rectangular coordinate system, a and B are two points on the coordinate axis that are not at the origin, point a is on the X axis, point B is on the Y axis, and there is a point C on the coordinate axis, so that
In the plane rectangular coordinate system, a and B are two points on the coordinate axis that are not at the origin, point a is on the X axis, point B is on the Y axis, and Ao is not equal to Bo. There is a point C on the coordinate axis, so that the triangle ABC is an isosceles triangle. How many C points are there?

There are two such C points, that is, on the X and Y axes respectively, connecting AB as his vertical bisector, and intersecting the coordinate axis at two points, that is, two C points

How to calculate the coordinates of a point on the space rectangular coordinate system after rotating according to the origin?

A new coordinate system ox'y'z 'is obtained by setting it in oxy coordinate system, the origin is fixed and the coordinate axis is rotated
The positive angles between axis ox 'and axis ox, oy and oz are α 1, β 1 and γ 1, respectively;
The positive angles between oy 'axis and ox, oy and oz axes are α 2, β 2 and γ 2, respectively;
The positive angles between axis oz 'and axes ox, oy and oz are α 3, β 3 and γ 3, respectively;
If the coordinates of m point in the coordinate system oxyz and ox'y'z are: (x, y, z) and (x ', y', Z ') respectively
Then the corresponding rotation transformation is as follows:
X=X'cos α1+Y'cos α2+Z'cos α3
Y=X'cos β1+Y'cos β2+Z'cos β3
Z=X'cos γ1+Y'cos γ2 +Z'cos γ3
perhaps
X'=Xcos α1+Ycos β1+Zcos γ1
Y'=Xcos α2+Ycos β2+Zcos γ2
Z'=Xcos α3+Ycos β3 +Zcos γ3