The point can be an actual Point drawn using the Point, Center Point tool from the Draw panel in Inventor, or it can be a corner of a solid body, the centerpoint of a circle, or the end of a line.

Start by clicking the point, then any face or plane to get a plane centered on your point and parallel to that plane —or, if the point is at the end of a line, click the line second to get a plane tangent to the line. If the plane you need is parallel to one of the origin planes, use the origin plane before In the image below, I’ve sketched a rectangle that is skewed to the origin, a circle, a line, and arc, and a point. I’ll create several examples using these shapes…

Clicking on the lower end of the line then the XZ Origin Plane gave me a plane at the end of the line parallel to the XZ Origin Plane…

Dragging the end of the line in a counterclockwise motion, then hitting the Local Update (lightning bolt at the top of the screen) shows that the plane remains associated with the end of the line, and is also still parallel to the XZ Origin Plane…

Now I’ll extrude the rectangle up a bit (and share the sketch so it remains visible), and create a plane by clicking on the centerpoint of the circle and the shaded small face on the extruded rectangle…

The other planes were dragged into position at by the points for clarity, this latest one was not…but  It makes absolutely no difference where the little representation is, or whether it is even visible. The next plane was created at the left end point of the arc and the XZ Origin Plane….

Again, the representation of the plane is not created at the end of the line, but in this instance, slicing thru the rectangular solid… and again, it matters not. The plane is present in the entire modelspace on that plane…not just where the indicator is.

the following plane was created by line and endpoint, which is exactly what it sounds like. I clicked on the line, then on the closer end of the line to create a plane perpendicular to the line, at the end of the line…

One last plane, this one is not created on a point, but I couldn’t resist. I extruded the circle up into a cylinder, then created a plane by clicking on the face of the cylinder and the shaded end of the rectangle. it created the plane that spans the cylinder and rectangle….

Ooops. missed one. The corners of the rectangle are points as well. The last plane was created by clicking on the XZ plane, which highlights it as can be seen below, and the corner seen below…

…to get the plane shown below, slicing through the cylinder….

Here is the example file in 2010 format. Enjoy.