Question

Point C does not lie on XY. Can point C lie in the same plane as XY?

Answer 1

Point C can lie in the same plane as XY even if it's not on line XY, it can be described by its Cartesian or polar coordinates in that plane.

Step-by-step explanation:

Yes, point C can still lie in the same plane as XY even though it is not on line segment XY. Imagine you have a flat surface, which represents the plane. No matter where you place a point on this surface, it lies within the plane, just like any point along line XY does. In the context of a Cartesian coordinate system, we can describe point C by its coordinates (x, y), even if it's not on XY. If we wish to visualize this in a three-dimensional space, we can include a z-coordinate (x, y, z), but if C is to be in the same plane as XY, its z-coordinate would be the same as that of the line XY (assuming the line has a constant z-coordinate).

In a scenario involving polar coordinates, the situation remains the same. The plane XY could be described by a radial distance and an angle, but point C would still have a place in the same plane via its own unique polar coordinates, irrespective of its positional relation to XY.

Answer 2

Assuming that XY refers to a line made by points X and Y and we have another point which is point C. Yes this is correct; point C can be in the same plane as XY but not necessarily lie on XY. This is because two points create a line while 3 non collinear points create a plane.