A transformation matrix will do that for you. You can define a matrix that defines the transformation from one coordinate system to another and then use that to transform each of your points.
Here's an example.
Let's assume I have a coordinate system like the one in your original description where positive X is to the left and positive Y is up. I have some points whose coordinates are defined relative to that coordinate system. I want to create those same points in Fusion but I know that coordinate system is different than the sketch coordinate system. In this sample, the coordinate system is not only oriented like I described, but the origin is 10 cm in the X direction of the sketch coordinate system. Here's a picture, where the coordinate system the points are defined in is purple and the sketch coordinate system is shown in green.

Here's the code. The original points are (1,1,0), (1,2,0), (1,3,0), and (1,4,0) and are defined relative to the purple coordinate system. In the code, the position and orientation of the purple coordinate system is defined. It then uses that to create a transformation matrix to go from that coordinate system to the sketch coordinate system. The points are then transformed and created in the sketch. They are positioned as shown in the picture. The (1,1,0) point now has the coordinate (9,1,0) after the transform has been applied.
I also draw some lines in the sketch so you can see where the X and Y axes are because Fusion doesn't show that.
def MatrixSample():
try:
des: adsk.fusion.Design = app.activeProduct
# Define the coordinate system the points are currently defined in where it
# is defined with respect to the sketch coordinate system.
origin = adsk.core.Point3D.create(10, 0, 0)
xDir = adsk.core.Vector3D.create(-1, 0, 0)
yDir = adsk.core.Vector3D.create(0, 1, 0)
points = []
points.append(adsk.core.Point3D.create(1, 1, 0))
points.append(adsk.core.Point3D.create(1, 2, 0))
points.append(adsk.core.Point3D.create(1, 3, 0))
points.append(adsk.core.Point3D.create(1, 4, 0))
# Define the matrix that describe the transform into sketch space.
otherCoordSys = adsk.core.Matrix3D.create()
zDir = xDir.crossProduct(yDir)
yDir = zDir.crossProduct(xDir)
otherCoordSys.setWithCoordinateSystem(origin, xDir, yDir, zDir)
# Invert it to shift it to the sketch coordinate system.
otherCoordSys.invert()
if app.activeEditObject.objectType != adsk.fusion.Sketch.classType():
ui.messageBox('A sketch must be active.')
return
sketch: adsk.fusion.Sketch = app.activeEditObject
for point in points:
# Transform the point.
point.transformBy(otherCoordSys)
# Create the point in the sketch.
sketch.sketchPoints.add(point)
# Draw the axes of the sketch coordinate system to be able to visualize it.
lines = sketch.sketchCurves.sketchLines
lines.addByTwoPoints(adsk.core.Point3D.create(0,0,0), adsk.core.Point3D.create(10,0,0))
lines.addByTwoPoints(adsk.core.Point3D.create(0,0,0), adsk.core.Point3D.create(0,5,0))
except:
ui.messageBox('Failed:\n{}'.format(traceback.format_exc()))
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Brian EkinsInventor and Fusion 360 API Expert
Website/Blog:
https://EkinsSolutions.com