If P is a point on the image with inverse scale function y = K / x, and perpendicular to X axis and Y axis respectively through P, the shadow area is 5, then the expression of inverse scale function

If P is a point on the image with inverse scale function y = K / x, and perpendicular to X axis and Y axis respectively through P, the shadow area is 5, then the expression of inverse scale function

y=5/x
y=-5/x

Given that the inverse scale function image passes through a (1,4), point P is also a point on the image and the distance to X axis is 2 (1), the analytic expression of inverse scale function is obtained
(2) Find the coordinates of point P
(3) Connect PA, Po and Ao, and find the area of triangle AOP

(1) Let y = K / X be the analytic expression of this inverse proportion function. Because the function image passes through point a (1,4), so: 4 = K / 1, that is, k = 4, so the analytic expression of this function is: y = 4 / X;
(2) In y = 4 / x, if y = 2, then x = 2, if y = - 2, then x = - 2, so the coordinates of point P are (2,2) or (- 2, - 2);
(3) When the coordinates of point P are (2,2), the equation of straight line AP is: y = 6-2x, let y = 0, get x = 3, so the line y = 6-2x intersects with X axis at (3,0), set it as point B, so: area of triangle AOP S1 = area of triangle AOB s-area of triangle POB S2 = (1 / 2) * 3 * 4 - (1 / 2) * 3 * 2 = 3; when the coordinates of point P are (- 2, - 2), the equation of straight line AP is: y = 2x + 2, let y = 0, get x = - 1, So the line y = 2x + 2 intersects with the X axis at (- 1,0) and is set as point C, so: the area of triangle AOP s = the area of triangle AOC S1 + the area of triangle POC S2 = (1 / 2) * | - 1 | * 4 + (1 / 2) * | - 1 | * | - 2 | = 3

How to solve the problem of inverse proportion function in grade two of junior high school

You may be asked to find the shadow area in the inverse proportion function. Sometimes, this kind of problem is similar, and some parallel problems can be used. All these problems need to be analyzed in detail. At the same time, we should make full use of the characteristics of the analytical formula. We may also give you a triangle or quadrilateral area product to find the analytical formula. In this kind of problem, you should remember that the triangle area is 2.1|k |, and the quadrilateral area is |k |
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