The image with known positive scale function y = 1 / 4x passes through point a (2, a) (1) The analytic expression of inverse scale function image passing through point a (2) If any point P in the image of the inverse scale function is taken as the PA ⊥ X axis and Pb ⊥ Y axis, the area of the rectangular OAPB can be calculated

The image with known positive scale function y = 1 / 4x passes through point a (2, a) (1) The analytic expression of inverse scale function image passing through point a (2) If any point P in the image of the inverse scale function is taken as the PA ⊥ X axis and Pb ⊥ Y axis, the area of the rectangular OAPB can be calculated

Solution (1): the image with positive scale function y = 1 / 4x passes through point a (2, a), and substituting x = 2, y = a into y = 1 / 4x, we get the following result:
a=1/4×2=1/2
So, the coordinate of point a is a (2,1 / 2)
Let the analytic expression of inverse proportion function be y = K / X. substituting x = 2, y = 1 / 2 into y = K / x, we can get the following result:
1/2=k/2
k=1
Therefore, the analytic expression of inverse scale function is y = 1 / X
Solution (2): in the inverse scale function y = 1 / x, k = 1
Area of rectangular OAPB = absolute value of abscissa value of point P × absolute value of ordinate value of point P = | K | = 1