points E or F
The key is that the image (triangle after rotation) and pre-image(triangle prior to rotation) will not touch each other. So let's look at the available options and see if they work or not.
point C - This is one of the vertexes of the triangle. If the triangle is rotated about this point, then this point will be a point of intersection between the pre-image and image. So this point won't work.
point D - This point is in the middle of the triangle. After rotating 180 degrees about this point, none of the vertexes will touch. However, there is a large area in common with both triangles that will be on top of each other. So this point won't work either.
point E - This point is below the pre-image triangle. If you rotate about this point, you'll get a new triangle that's pointing downwards and will at a lower Y value than the pre-image triangle. No point on or in this new triangle will overlap any point of the original triangle. It works, so point E is one of the possible solutions.
point F - This point is far to the right of the original pre-image. If you rotate about this point, the resulting triangle will be further to the right and will not intersect the original triangle. So this point also works and is one of the possible solutions.
