The relationship between triangle area and K value in inverse scale function image I know that the area of the triangle enclosed by the points on the image and the coordinate axis perpendicular to the inverse scale function is equal to half of the area of the triangle. But if there is a point on the image, another point is at the origin, and the three sides are not perpendicular to the coordinate axis, is this conclusion true?

The relationship between triangle area and K value in inverse scale function image I know that the area of the triangle enclosed by the points on the image and the coordinate axis perpendicular to the inverse scale function is equal to half of the area of the triangle. But if there is a point on the image, another point is at the origin, and the three sides are not perpendicular to the coordinate axis, is this conclusion true?

The conclusion should not hold. Because your condition is too wide, you only know that one point is on the hyperbola, the other point is at the origin, and the position of the third point is uncertain. Even if the third point is also on the coordinate axis, this conclusion may not hold